Harder because the methods being asked are nonoptimal. I kind of read this as some questions on a homework assignment in HS where the teacher didn't put any thought into which equations they wrote.
Yeah, I've been out of school for a few years and haven't really had to solve any equations like that in a while, but my mind was pretty quick to jump to exactly that. I'm not super smart, it's just super simple.
Best way to solve x² + x + 1 = 0
Multiply by (x-1) and distribute (or if you know that this is a formula..), of course x ≠ 1
x³ - 1 = 0
x³ = e^(2iπ + 2πk)
x = cis(⅔π(k+1)) 0≤k≤2
These spit out our solutions, except notice that for k = 2 we get x = 1 which is the extraneous solution we got from multiplying by (x-1).
Ok if you know to multiply by x - 1 then you already recognize it as the polynomial for the cube roots of unity and you can just keep to e^(2πi/3) and e^(4πi/3)
with the power of my two human eyes
Jokes aside, I’m probably not the only one that does this, but I always check if zero or 1 solves the question first since it does fairly often on math exams
Imagine crying because you need to use a fcking formula that takes 5s to write
Imagine crying because you need to complete the square of one of the simplest polynomial
I have the equivalent math education to first-year undergrad, which isn't a lot, but some people are not very good at math and you shouldn't make fun of them for being badly educated
Not to mention a lot of people simply don't have the same mental capacity to deal with abstractions like this. I don't mean that in a judgemental way or anything, just that everyone has a different brain. For example, a surprisingly large percentage of people don't even have an inner monologue, and a also surprisingly large percentage don't have the ability to visualize things mentally. Like there's no ability to picture things in their mind at all.
Plenty of people are built for math/STEM majors, but equally plenty of people are built to be other things. Nobody is more important or better than anyone else just because they can remember polynomial equations.
Completing the square almost stopped me from passing diffeq after having passed calc 1-3.
I hadn’t had to fuck with algebra like that for 10 years at that point, my knowledge of that black magic fuckery was entirely gone.
That, and partial fraction decomposition. Ugh. Yuck.
That’s one opinion.
I worked my absolute dick off and got As and Bs, as a returning student the algebra from high school was not strong in my brain anymore.
I spent hours and hours of effort studying the material, and my hard work paid off.
But sure, I didn’t deserve it because PFD was hard for me, and factoring polynomials was ingrained into me without completing the square. Oh well.
lol fuck off.
Remind me where you needed PFD or completing the square whatsoever as a mandatory requirement for calc 1-3. It literally never came up. I didn’t *need* those things till diff, and the class was so fast paced that I struggled to pick it up in time to keep up with the course work.
Take your shitty opinions and go rain on someone else’s parade. I’m not going to lose a minute of sleep over what someone’s gatekeepy opinions about mathematics are on a meme sub no less.
Like what percentage of population? Also what tests show evidence of that. Like how do you prove someone has inner monologue and also how do you define it? Like if I sometimes think to myself "You idiot! It was so obvious" Is that considered inner monologue? About visualization I really can't tell. Like I can visualize simple things but if I e.g. want to visualize someone I mostly can do it for a split second unless I really focus. I really got curious lol. That 2am curiosity kicked in.
I thought it was common knowledge, my bad. I see it posted on reddit pretty often.
The condition of not having a "mind's eye" is called aphantasia. It is estimated to affect as many as 1 in 25 people (4%). These people are often surprised when they learn that other people can visualize/picture things in their mind.
https://fortune.com/well/2023/05/23/what-is-aphantasia-people-cant-visualize-images-in-minds-eye-brain/
As many as 50% of people have no internal monologue. Some estimates say 70%, but even I am having a hard time believing that.
https://eccentricemmie.medium.com/only-30-50-of-people-have-an-internal-monologue-b75125ca5694#:~:text=However%2C%20did%20you%20know%20that,this%20fact%20absolutely%20baffles%20me.
damn, thanks. this is leading me down a rabbit hole. how is complicated decision making done without internal dialog? how does one remember past events without visualizing them? how does it affect trauma and flashbacks? so many questions..
The brain is an amazing and incredible thing! As for how decisions are made... I feel like a good analogy is when you have a computer without a monitor. Processing can still happen, decisions can still take place, you just can't see what's being done. Which limits you, because you can't really Photoshop a picture without seeing what you're doing. But you definitely can have programs running in the background that are accomplishing tasks, you know. This is just an analogy, but I feel like it's the closest we can come to understanding what it's like without being able to see in their mind. Like I said, brains are amazing things, and we still have much to learn.
Sorry i realize now i sounded like an ass
If it helps, its possible to sing the quadratic formula to the tune of pop goes the weasel. Ive been singing this tune in my head for years:
X is equal to negative b
Plus or minus the square root
B squared minus four a c
All over 2 a
I don't struggle at all with the quadratic formula lol, I'm just saying that it might be a bit rude for them. I consider myself a fast learner in math, but not everyone's like you or me
I don't agree that you sounded like an ass, the person you were replying to is way in their heads. This is literally taught to teens as you said, and all in all not all that hard. If this is hard, then FFS, everything in math would be extremely hard and worth crying over.
I'm french and I personnally learned quadratics in the 2nd last year of high school and it was outside the hardest math course (which consists of mainly arithmetic and linear algebra). But yeah it's still late compared to the states but hey on the bright side, we do pretty much the entirety of calculus 1 during our 2 last years of high school.
Haha, I'm literally tutoring a 15 year old underpriviledged kid in India (who's parents are a taxi driver and a cook), and he learnt to do all 3 methods after some practice. PhD lol
I also know how to do the quadratic formula. I learned it in 6th grade, actually. But not everyone's like you or me lmfao, I'm just advocating for being a nice person
Was it because you knew how much wasted time it would take to learn how to calculate quickly and accurately or because you’d never trust something as temporary and imperfect as imagination and memory to accurately work through a problem?
I can relate with a little OCPD thrown in for good measure which made the logic and mechanics of equations fucking exquisite and “perfect” to me… something that doesn’t exist in the real world no matter how much you clean, tinker, design, program, or create.
In the United States, quadratic equations are often taught in Math II high school courses.
I personally learned the quadratic formula around fifth or sixth grade through self-study, but most Americans suck at math.
So do they just reiterate multiplication, division, addition and subtraction for 9 years? Because God knows they aren't teaching statistics, probability, and combinotorics which are the only fields I can think of that don't require algebra. Wtf that sounds boring as fuck how do you survive?
(I guess you can teach graph theory before algebra, theoretically. And obviously set theory but nobody teaches that until university)
I took algebra 1 in 8th grade and, for me, 1st-5th were literally just arithmetic, I didn't really have a math class in 6th grade (I had the same teacher and class for math and science, but the teacher used both blocks to teach science), and 7th grade was probably "pre-algebra" or something. I'm now a senior in highschool taking calculus. I know people my grade who are doing the math I did as a freshman/sophomore and I have no idea how it took them 11 years to get to that point.
Yeah that was my experience too, and I was mad that elementary school math classes wasted so much time reiterating stuff. Algebra should start in 3rd grade honestly but I understand that it usually starts in middle school. High school is beyond my comprehension
Kindergarten involves learning to count, mostly by ones and fives, from what I recall.
First grade was learning perimeters, and number composition (so breaking numbers like 15,345 into 10,000 + 5,000 + 300 + 40 + 5) and further introduction to addition and subtraction (mostly one-digit numbers).
Second grade starts learning addition/subtraction with 2 or more digits, plus multiplication, and a taster of division.
Third grade goes in hard on multiplication with the introduction of finding areas of 2D shapes, and begins teaching long division in earnest, also the order of operations is introduced in this grade.
Fourth grade refines on the stuff from before and goes in harder on long division, plus introduces multiplication and division of decimals.
Fifth grade is honing in on the decimals and preparing you to understand more complex word problems, basically being the introduction to solving equations for variables (which was rough for me since I'm autistic).
Sixth grade all but fully introduces solving for variables with even more complex word problems, and I vaguely remember literally being given some practice questions where we were literally solving a written equation, rather than "jimmy has seven billion water buffalo" stuff.
Seventh grade, depending on if you're smart enough, you either get to go to "Pre-Algebra Concepts" (which is what my middle school called it), or straight to algebra.
Eighth grade, if you were smart enough but didn't get to take algebra 1 in seventh, you can take it now. Otherwise it's to a class called "Algebra Concepts", and the only thing i can remember from that class is learning factorials because it was the only new concept to me. Also, if you got algebra 1 during seventh grade, you get to walk to the high school for a period every day to take algebra 2 (one of the kids i was in band with did this).
9th grade is where most students' algebra education proper begins.
10th you take algebra 2 and usually geometry, but you can save that for later
at this point, you're optionally done with math classes, but you can choose to go on and get some more math credits with prob&stats or pre-calc in 11th. and senior year you can take calc. I guess you can technically take calculus whenever if you can keep up. When I was a junior I tried to take the physics course, but it was calc-based and I got steam-rolled. They only implemented an algebra-based physics class after I graduated.
This is the American mathematical education system in a nutshell (plus some editorialization). I'm sure it's slightly different in other parts of the country, but I think I got the key notes.
I attend physics at university but I have never even heard about the "complete the square" method. I did look up now and while I do understand the concept I don't think I will ever use it. Using other formulas is just way more simple.
I only ever remember completing the square being used in calculus later on (one of the integration methods I think) but besides that I have never ran into a situation where it's useful.
Technically completing the square is just the same as using the formula since it’s the methou you use to prove this formula (or at least it’s the more popular method to prove the formula because I don’t know another method)
Complete the square. It is called this, because the steps you take makes a square, when you look at what it does via geometry.
Adding (b/2a)^2 to both sides is the first step. Don’t feel like typing the rest, because I don’t feel like it.
Quadratic formula was derived from it. So, it is required to get to the formula, but it is also used when changing the form the quadratic equation is in (standard into locus or vertex). It is also used when making the general equation of a circle (unfactored into the general equation). Complete the square was used when we wanted to solve cubics. At least the idea was, we were instead completing the cube.
There’re probably uses that I don’t know. But, it was quite an amazing thing to be found.
It has many practical uses. Such as what I said in my comment. Plus it is a method that helps people understand why the quadratic formula works. It is an important part of circle and quadratic equations, and understanding their properties. Really, the quadratic formula is the least important thing it achieves, as it only removes a couple of steps from complete the square.
When it comes down to it, completing the square is just finding a way of transforming the equation:
Ax^(2) + Bx + C = 0
Which can be difficult to solve, into another equation:
(x + λ)^(2) = β
Which is easily solved as:
x = -λ ± √β
To determine what λ and β are, we first divide the first equation by 'A' (prima facie, A ≠ 0 so we are allowed to do this). This gives:
x^(2) + (B/A) x + C/A = 0
--> x^(2) + (B/A) x = -C/A
Now we'd like to be able to add some term to the lefthand side (and the RHS to balance the equation) such that the LHS is a perfect square. Let's try 'FOIL'-ing one particular perfect square:
(x+B/2A)^(2) = x^(2) + (B/A) x + (B/2A)^2 (check this for yourself).
So now if we add (B/2A)^(2) to both sides of our equation, we end up with:
x^(2) + (B/A) x + (B/2A)^(2) = (B/2A)^(2) - C/A
And since we established the LHS is now a perfect sqaure:
--> (x + B/2A)^(2) = (B/2A)^2 - C/A
And remember the entire reason we wanted to get it into this form is to make the solution obvious. In particular, with our names for the terms given earlier, we notice:
λ = B/2A
β = (B/2A)^2 - C/A
And to reiterate, our two solutions are:
x = -λ ± √β
All that's left is to simplify this to make it prettier. λ is as simple as it can be already, but notice we can expand β as:
β = (B/2A)^(2) - C/A = B^(2)/4A^(2) - C/A
Find a common denominator:
--> β = B^(2)/4A^2 - 4A^(2)C/(4A^(2))A = B^(2)/4A^(2) - 4AC/4A^(2)
--> √β = √(B^(2)-4AC)/√(4A^(2)) = √(B^(2) - 4AC)/2A
Now writing our full solution:
--> x = [-B ± √(B^(2) - 4AC)]/2A
Look familiar?
Assuming xeR
a) x=2
b) x=-2 \/ x=-1
c) Fuck u, will write it as: (x+1/2)^2 +3/4=0 —> (x+1/2)^2 can’t be negative, and so: (x~[0–>]) +3/4 = 0 —> x~[0–>] = -3/4
x which has to be positive, equals something negative. x can therefore not exist withing real numbers. Im not smart enough to perfect square shit, or deal with imaginary values, so there ya go.
when taking the square root of a negative number, the first thing you do is pull the negative sign out and make it i, then take the root, and you get xi where x is any number
Solving by completing squares was my bane in school, and to this day I have no clue how it's done. And I'm an engineer. My brain automatically shuts off whenever this question comes up.
Not gonna lie I went through a whole ass math degree without completing the square except for in middle school when I was taught how to do it so I forgot how. Quadratic formula always works so I just used that any time I had a calculator, which was most of the time. I could look up how to complete the square and I'm sure it wouldn't be too hard, but why would I bother? Especially since I don't even use my math degree.
# Using a \# mark at the start of a line will make it a heading.
## Using 2, you get slightly smaller, and not bold.
### Using 3, you get smaller, bold text
#### Using 4, you get smaller than 3, but not bold
##### Using 5 makes the text yet smaller and emboldens.
###### Using 6 makes the text normal size, but underlines.
OHHH I FORGOT TO CHANGE THE - IN + I DID 2X=0-4 I'M A FUCKEN IDIOT (and that's why i prefer geometry to algebra) which now means 2x=4 hence x=2 i can't think properly late, especially algebra.
Is the joke that the third one doesn't have real valued roots or am i missing something?
yes yes it is
But one can still complete the square. Not sure how this is a joke other than the format shows they are progressively harder problems.
Harder because the methods being asked are nonoptimal. I kind of read this as some questions on a homework assignment in HS where the teacher didn't put any thought into which equations they wrote.
You can still complete the square x^2 + x + 1=0 x^2 + x = -1 x^2 + x +1/4 = -1+1/4 (x+1/2)^2 = -3/4 x+1/2 = +-sqrt(-3/4) x=(-1+-sqrt(3)i)/2
painfulass process tho
No more than the quadratic formula
there's all the fractions and shit
Yeah, it's called math
but it's harder
It's literally the same shit
but there's no fraction operations in the quad formula
x=(-b+-sqrt(b^2 -4ac))/2a What you do call the /2a?
Well yeah its a quadratic so it has two solutions, thats why i said no real valued solutions because all solutions are complex valued.
I like completing the square moree
It’s a nice method but if b is odd then you don’t just have integers and it can be annoying
multiply by 4
Holy fucking shit. I never thought of this. High school has failed me once again
Wait, how does this help?
Try it oit
I did, really cool way of solving this problem. I also would've never thought abt this lol.
Me too, part of the reason I like math is because of things like this
2(b/2) ?
I really hate the solve by formula for the second one because I want to just immediately write (x+1)(x+2)=0; x=-1 or x=-2
Look at you doing in-head calculations
There's a theorem that states every polynomial in an exam has roots 1, -1, 2 or -2. Proof is left as an exercise for the reader.
I say to expand the bounds of this theorem, experience has taught me roots of 3 and -3 aren't forbidden.
I have to admit that I usually try these if the equation seems too long; to solve it faster
hahahah, classic in Differential Equations
That's called mental...isn't it?
Yeah, I've been out of school for a few years and haven't really had to solve any equations like that in a while, but my mind was pretty quick to jump to exactly that. I'm not super smart, it's just super simple.
I just write my usual solution because i have memorised it but not enough to memorize the answer
Yea, most of the time the difference between b and c is 1 you can very easily find the factors
Best way to solve x² + x + 1 = 0 Multiply by (x-1) and distribute (or if you know that this is a formula..), of course x ≠ 1 x³ - 1 = 0 x³ = e^(2iπ + 2πk) x = cis(⅔π(k+1)) 0≤k≤2 These spit out our solutions, except notice that for k = 2 we get x = 1 which is the extraneous solution we got from multiplying by (x-1).
Ok if you know to multiply by x - 1 then you already recognize it as the polynomial for the cube roots of unity and you can just keep to e^(2πi/3) and e^(4πi/3)
I’m taking math 3 right now, those equations look scary
How do you "know" x isnt =1, do you just test it before ?
with the power of my two human eyes Jokes aside, I’m probably not the only one that does this, but I always check if zero or 1 solves the question first since it does fairly often on math exams
Indeed, those are the easiest numbers to test (followed by a (-1)), and I also do this very often!
easy to test and often a solution especially on questions that want you to find like five solutions I can at least get credit for -1 0 and 1
Gonna be real, I can solve by almost everything but complete the square because I never remember the steps
Just write the general (a+b)^2 = a^2 + 2ab + b^2 and compare. There's no need for "steps".
Imagine crying because you need to use a fcking formula that takes 5s to write Imagine crying because you need to complete the square of one of the simplest polynomial
Imagine making fun of people for not being at the same math level as you, but still trying to be a part of the community.
no need to make fun of them, not everyone's a math PhD
PhD? dude its a formula used by pre-teens. the hardest component is finding the root of an integer
I have the equivalent math education to first-year undergrad, which isn't a lot, but some people are not very good at math and you shouldn't make fun of them for being badly educated
> some people are not very good at math Yes, we are called engineers.
The answer is a gun, and if that don't work, use more gun.
Not to mention a lot of people simply don't have the same mental capacity to deal with abstractions like this. I don't mean that in a judgemental way or anything, just that everyone has a different brain. For example, a surprisingly large percentage of people don't even have an inner monologue, and a also surprisingly large percentage don't have the ability to visualize things mentally. Like there's no ability to picture things in their mind at all. Plenty of people are built for math/STEM majors, but equally plenty of people are built to be other things. Nobody is more important or better than anyone else just because they can remember polynomial equations.
Completing the square almost stopped me from passing diffeq after having passed calc 1-3. I hadn’t had to fuck with algebra like that for 10 years at that point, my knowledge of that black magic fuckery was entirely gone. That, and partial fraction decomposition. Ugh. Yuck.
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That’s one opinion. I worked my absolute dick off and got As and Bs, as a returning student the algebra from high school was not strong in my brain anymore. I spent hours and hours of effort studying the material, and my hard work paid off. But sure, I didn’t deserve it because PFD was hard for me, and factoring polynomials was ingrained into me without completing the square. Oh well.
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lol fuck off. Remind me where you needed PFD or completing the square whatsoever as a mandatory requirement for calc 1-3. It literally never came up. I didn’t *need* those things till diff, and the class was so fast paced that I struggled to pick it up in time to keep up with the course work. Take your shitty opinions and go rain on someone else’s parade. I’m not going to lose a minute of sleep over what someone’s gatekeepy opinions about mathematics are on a meme sub no less.
Spittin fax bro
Like what percentage of population? Also what tests show evidence of that. Like how do you prove someone has inner monologue and also how do you define it? Like if I sometimes think to myself "You idiot! It was so obvious" Is that considered inner monologue? About visualization I really can't tell. Like I can visualize simple things but if I e.g. want to visualize someone I mostly can do it for a split second unless I really focus. I really got curious lol. That 2am curiosity kicked in.
I thought it was common knowledge, my bad. I see it posted on reddit pretty often. The condition of not having a "mind's eye" is called aphantasia. It is estimated to affect as many as 1 in 25 people (4%). These people are often surprised when they learn that other people can visualize/picture things in their mind. https://fortune.com/well/2023/05/23/what-is-aphantasia-people-cant-visualize-images-in-minds-eye-brain/ As many as 50% of people have no internal monologue. Some estimates say 70%, but even I am having a hard time believing that. https://eccentricemmie.medium.com/only-30-50-of-people-have-an-internal-monologue-b75125ca5694#:~:text=However%2C%20did%20you%20know%20that,this%20fact%20absolutely%20baffles%20me.
damn, thanks. this is leading me down a rabbit hole. how is complicated decision making done without internal dialog? how does one remember past events without visualizing them? how does it affect trauma and flashbacks? so many questions..
The brain is an amazing and incredible thing! As for how decisions are made... I feel like a good analogy is when you have a computer without a monitor. Processing can still happen, decisions can still take place, you just can't see what's being done. Which limits you, because you can't really Photoshop a picture without seeing what you're doing. But you definitely can have programs running in the background that are accomplishing tasks, you know. This is just an analogy, but I feel like it's the closest we can come to understanding what it's like without being able to see in their mind. Like I said, brains are amazing things, and we still have much to learn.
totally. that analogy makes a lot of sense, even though i can't fully comprehend what that looks/feels like. fascinating stuff!
Sorry i realize now i sounded like an ass If it helps, its possible to sing the quadratic formula to the tune of pop goes the weasel. Ive been singing this tune in my head for years: X is equal to negative b Plus or minus the square root B squared minus four a c All over 2 a
I don't struggle at all with the quadratic formula lol, I'm just saying that it might be a bit rude for them. I consider myself a fast learner in math, but not everyone's like you or me
bold of you to assume im a fast learner in math lmao
I don't agree that you sounded like an ass, the person you were replying to is way in their heads. This is literally taught to teens as you said, and all in all not all that hard. If this is hard, then FFS, everything in math would be extremely hard and worth crying over.
the meme is no real value, that's it. Not because they have to use a formula
Pre teens? In France we do this in the last year of high school for those that picked the hardest math course possible
I'm french and I personnally learned quadratics in the 2nd last year of high school and it was outside the hardest math course (which consists of mainly arithmetic and linear algebra). But yeah it's still late compared to the states but hey on the bright side, we do pretty much the entirety of calculus 1 during our 2 last years of high school.
Imaginary numbers are only taught in terminale Maths Expertes, the b² - 4ac thing in première spé maths
Yeah it's for complex numbers, arithmetic and linear algebra (matrices) but you don't need to learn quadratics (thankfully)
Haha, I'm literally tutoring a 15 year old underpriviledged kid in India (who's parents are a taxi driver and a cook), and he learnt to do all 3 methods after some practice. PhD lol
I also know how to do the quadratic formula. I learned it in 6th grade, actually. But not everyone's like you or me lmfao, I'm just advocating for being a nice person
Nice flex bro
I have a math phd and I use my fingers to add numbers.
Was it because you knew how much wasted time it would take to learn how to calculate quickly and accurately or because you’d never trust something as temporary and imperfect as imagination and memory to accurately work through a problem?
I have adhd, also I almost never need to calculate things by hand so thats a pretty unused brain part
I can relate with a little OCPD thrown in for good measure which made the logic and mechanics of equations fucking exquisite and “perfect” to me… something that doesn’t exist in the real world no matter how much you clean, tinker, design, program, or create.
This is r/mathmemes, not r/middleschoolmemes
First of all this is 10th grade math Second of all 10th grade math is still math
Who's doing quadratics in 10th grade? Tf did you learn the first 9 years? Do they just only teach math every other year in your region or something?
In the United States, quadratic equations are often taught in Math II high school courses. I personally learned the quadratic formula around fifth or sixth grade through self-study, but most Americans suck at math.
It's a miracle y'all still have any cultural influence at all
Your average American is dumb as hell, there's a reason the average SAT score is like 1050
Some places in the US don't start teaching algebra until 10th grade.
So do they just reiterate multiplication, division, addition and subtraction for 9 years? Because God knows they aren't teaching statistics, probability, and combinotorics which are the only fields I can think of that don't require algebra. Wtf that sounds boring as fuck how do you survive? (I guess you can teach graph theory before algebra, theoretically. And obviously set theory but nobody teaches that until university)
I took algebra 1 in 8th grade and, for me, 1st-5th were literally just arithmetic, I didn't really have a math class in 6th grade (I had the same teacher and class for math and science, but the teacher used both blocks to teach science), and 7th grade was probably "pre-algebra" or something. I'm now a senior in highschool taking calculus. I know people my grade who are doing the math I did as a freshman/sophomore and I have no idea how it took them 11 years to get to that point.
Yeah that was my experience too, and I was mad that elementary school math classes wasted so much time reiterating stuff. Algebra should start in 3rd grade honestly but I understand that it usually starts in middle school. High school is beyond my comprehension
Kindergarten involves learning to count, mostly by ones and fives, from what I recall. First grade was learning perimeters, and number composition (so breaking numbers like 15,345 into 10,000 + 5,000 + 300 + 40 + 5) and further introduction to addition and subtraction (mostly one-digit numbers). Second grade starts learning addition/subtraction with 2 or more digits, plus multiplication, and a taster of division. Third grade goes in hard on multiplication with the introduction of finding areas of 2D shapes, and begins teaching long division in earnest, also the order of operations is introduced in this grade. Fourth grade refines on the stuff from before and goes in harder on long division, plus introduces multiplication and division of decimals. Fifth grade is honing in on the decimals and preparing you to understand more complex word problems, basically being the introduction to solving equations for variables (which was rough for me since I'm autistic). Sixth grade all but fully introduces solving for variables with even more complex word problems, and I vaguely remember literally being given some practice questions where we were literally solving a written equation, rather than "jimmy has seven billion water buffalo" stuff. Seventh grade, depending on if you're smart enough, you either get to go to "Pre-Algebra Concepts" (which is what my middle school called it), or straight to algebra. Eighth grade, if you were smart enough but didn't get to take algebra 1 in seventh, you can take it now. Otherwise it's to a class called "Algebra Concepts", and the only thing i can remember from that class is learning factorials because it was the only new concept to me. Also, if you got algebra 1 during seventh grade, you get to walk to the high school for a period every day to take algebra 2 (one of the kids i was in band with did this). 9th grade is where most students' algebra education proper begins. 10th you take algebra 2 and usually geometry, but you can save that for later at this point, you're optionally done with math classes, but you can choose to go on and get some more math credits with prob&stats or pre-calc in 11th. and senior year you can take calc. I guess you can technically take calculus whenever if you can keep up. When I was a junior I tried to take the physics course, but it was calc-based and I got steam-rolled. They only implemented an algebra-based physics class after I graduated. This is the American mathematical education system in a nutshell (plus some editorialization). I'm sure it's slightly different in other parts of the country, but I think I got the key notes.
PhD probably doesn't remember the formula lol, they are doing other shit and probably wouldn't be such an ass about it like the other guy
This is 8th or 9th grade math
10th grade, I think. I personally learned it by self studying much earlier
Bruh somehow completing the square is so hard for me like other methods work why can’t I use those instead
I attend physics at university but I have never even heard about the "complete the square" method. I did look up now and while I do understand the concept I don't think I will ever use it. Using other formulas is just way more simple.
I only ever remember completing the square being used in calculus later on (one of the integration methods I think) but besides that I have never ran into a situation where it's useful.
Technically completing the square is just the same as using the formula since it’s the methou you use to prove this formula (or at least it’s the more popular method to prove the formula because I don’t know another method)
If you get into theoretical physics you'll need to know how to complete the square to evaluate gaussian integrals, which come up a lot.
the cubic formula however...
Complete the what now?
Complete the square. It is called this, because the steps you take makes a square, when you look at what it does via geometry. Adding (b/2a)^2 to both sides is the first step. Don’t feel like typing the rest, because I don’t feel like it.
Sounds silly why not just use the formula
Quadratic formula was derived from it. So, it is required to get to the formula, but it is also used when changing the form the quadratic equation is in (standard into locus or vertex). It is also used when making the general equation of a circle (unfactored into the general equation). Complete the square was used when we wanted to solve cubics. At least the idea was, we were instead completing the cube. There’re probably uses that I don’t know. But, it was quite an amazing thing to be found.
Aw so it was used in developing the quadratic formula. No practical so far it seems.
Pretty easy to do and worth it in order to easily find the vertex without resorting to other formulae. Far from impractical in my opinion.
"resorting" lmao
All I'm saying is that it's useful to know, especially the geometric proof. If you don't know it, fret not! You can easily learn, I'm sure :)
Why would I lean such a silly method when the quedric formula exist
Alright, remain ignorant, doesn't affect me :)
It has many practical uses. Such as what I said in my comment. Plus it is a method that helps people understand why the quadratic formula works. It is an important part of circle and quadratic equations, and understanding their properties. Really, the quadratic formula is the least important thing it achieves, as it only removes a couple of steps from complete the square.
What's completing the square?
When it comes down to it, completing the square is just finding a way of transforming the equation: Ax^(2) + Bx + C = 0 Which can be difficult to solve, into another equation: (x + λ)^(2) = β Which is easily solved as: x = -λ ± √β To determine what λ and β are, we first divide the first equation by 'A' (prima facie, A ≠ 0 so we are allowed to do this). This gives: x^(2) + (B/A) x + C/A = 0 --> x^(2) + (B/A) x = -C/A Now we'd like to be able to add some term to the lefthand side (and the RHS to balance the equation) such that the LHS is a perfect square. Let's try 'FOIL'-ing one particular perfect square: (x+B/2A)^(2) = x^(2) + (B/A) x + (B/2A)^2 (check this for yourself). So now if we add (B/2A)^(2) to both sides of our equation, we end up with: x^(2) + (B/A) x + (B/2A)^(2) = (B/2A)^(2) - C/A And since we established the LHS is now a perfect sqaure: --> (x + B/2A)^(2) = (B/2A)^2 - C/A And remember the entire reason we wanted to get it into this form is to make the solution obvious. In particular, with our names for the terms given earlier, we notice: λ = B/2A β = (B/2A)^2 - C/A And to reiterate, our two solutions are: x = -λ ± √β All that's left is to simplify this to make it prettier. λ is as simple as it can be already, but notice we can expand β as: β = (B/2A)^(2) - C/A = B^(2)/4A^(2) - C/A Find a common denominator: --> β = B^(2)/4A^2 - 4A^(2)C/(4A^(2))A = B^(2)/4A^(2) - 4AC/4A^(2) --> √β = √(B^(2)-4AC)/√(4A^(2)) = √(B^(2) - 4AC)/2A Now writing our full solution: --> x = [-B ± √(B^(2) - 4AC)]/2A Look familiar?
This: https://www.mathsisfun.com/algebra/completing-square.html (I won't try to explain it because this is my first time hearing about it as well.)
Thank you for the link!
Kinda just a short way to find the turning point of a quadratic
“Solve by-“ I’ll solve it however I want fuck off
x\^2 + x + 1 = 0 x\^2 + x = -1 x\^2 + x + 1/4 = -1/2 (x+1/2)\^2=-1/2 x+1/2 = sqrt(-1/2) x+1/2 = sqrt(1/2)i x=-1/2±sqrt(1/2)i
I think you messed up on the right side in line 3. It should be: x^2 + x + (1/2)^2 = -1 + (1/2)^2 (x+1/2)^2 = -3/4 x = - 1/2 +- (sqrt(3)/2)i
You're right, I plugged in the answers to check.
delta my beloved
Solve by plotting it and assuming the teacher used integer roots
Im too stupid to understand the meme but isn’t x=2? Or am I more stupid than I thought?
Top has solutions x = 2, -2, middle -2, -1, bottom has no real solutions.
This is so fucking true
Honestly don't remember learning the "complete the square" method in school, seems so primitive.
(x+1)^2 -x
Assuming xeR a) x=2 b) x=-2 \/ x=-1 c) Fuck u, will write it as: (x+1/2)^2 +3/4=0 —> (x+1/2)^2 can’t be negative, and so: (x~[0–>]) +3/4 = 0 —> x~[0–>] = -3/4 x which has to be positive, equals something negative. x can therefore not exist withing real numbers. Im not smart enough to perfect square shit, or deal with imaginary values, so there ya go.
when taking the square root of a negative number, the first thing you do is pull the negative sign out and make it i, then take the root, and you get xi where x is any number
I’ve taken calc 2 (and did very well in it) but I still don’t know how to complete the square
quadratic formula exists for a reason
Solve using Newton-Raphson
Sometimes I have the urge to just strangle the quadratic formula
Solving by completing squares was my bane in school, and to this day I have no clue how it's done. And I'm an engineer. My brain automatically shuts off whenever this question comes up.
Well, what's the joke here though?
Not gonna lie I went through a whole ass math degree without completing the square except for in middle school when I was taught how to do it so I forgot how. Quadratic formula always works so I just used that any time I had a calculator, which was most of the time. I could look up how to complete the square and I'm sure it wouldn't be too hard, but why would I bother? Especially since I don't even use my math degree.
#3 is (X-i)^2?
Yo whys the text so big
# Using a \# mark at the start of a line will make it a heading. ## Using 2, you get slightly smaller, and not bold. ### Using 3, you get smaller, bold text #### Using 4, you get smaller than 3, but not bold ##### Using 5 makes the text yet smaller and emboldens. ###### Using 6 makes the text normal size, but underlines.
Just take the derivative easy…
Completing the square is better than the formula
when doing CTS: "this will cost us 51 years"
the answer is 3. because 1+1. thank you common core
Guys, what does completing the square look like? (I'm not native in english, so I will probably know this method, but not the name)
Po-Shen Loh method ftw
Just wait man
I never understood how to complete the square. Formula ftw
I believe the third one has the golden ratio as the solution for x but I'm not entirely sure. That might be x^2 +x-1=0 or x^2 -x+1=0.
I am stupid, but the first one comes as x=-4???
X is 2 or -2 X^2 -4=0 This simplified is (x+2)(x-2)=0 So plug both in to check 2^2-4=0, which is 4-4=0 -2^2-4=0, whish is also 4-4=0
Ok, yes, I'm stupid, and it's too late for me to understand this, I'll check it again tomorrow morning, thanks.
No problem!
OHHH I FORGOT TO CHANGE THE - IN + I DID 2X=0-4 I'M A FUCKEN IDIOT (and that's why i prefer geometry to algebra) which now means 2x=4 hence x=2 i can't think properly late, especially algebra.