3 ways to "complete the square"

[@blackpenredpen]

Have you impressed your teachers (or students) yet???

[@Ashmit_1729]

Yes by factoring 2

[@davidbrisbane7206]

Yes indeed. When I showed them how to use Wolfram Alpha to solve quatratic equations 😁.

[@أميرالبلابل]

Yeah, when I correct my teacher hahahah

[@invaderzim6842]

Hi ,blackpenredpen!I really enjoy your content. I’ll very much appreciate if u can solve me this problem Find x for:2^((sin(x))^2014)-2^((cos(x))^2014)=(cos(2x))^2013 I know it is a tough problem ,but I really want to know the way to solve this kind of problem 😅

[@sbusisoquintin8004]

Not yet we are waiting for them😅💯 Support from South Africa🇿🇦

[@shaurya1616]

I think his immense knowledge comes from the pokeball.

[@yensteel]

Agreed

[@mama5402]

I guess that's why he looks like a pokemon xd...

[@arjunsahu2543]

😂🤣🤣

[@williamsmamanimamani846]

Estoy totalmente de acuerdo, mi estimado

[@xxmysticexpertxx113]

Pikachu tellin him the answers

[@markdougherty8203]

Method 3 is just completing the square from the other side. By symmetry it works the same. It's a cool trick though, because most people don't expect it. I have surprised people with it before. Obviously it's more convenient if the units term is a perfect square.

[@AliKhanMaths]

I love the second way the most - looks so clean! You've really inspired me to share my maths tricks too!

[@MathAdam]

Next video: 3 Ways to Complete the Pikachu

[@anshumanagrawal346]

Yeesss

[@shuvo1562]

Type 3 seems new to me!Every time I learn something new from your videos.

[@beaming_sparkling_trash261]

I'm in love w the third method

[@alpcanakaydn6986]

additional soluiton: if we multiply each side by 2 it becomes 4x²+12x+18=0 if we complete the perfect square it becomes (2x+3)²+9=0

[@Leeanne750]

Multiplying by "4a" is safe. (In this case, 8). It will work all the time, not only in this example. ax^2 + bx +c =0 4a^2x^2 + 4abx = -4ac (2ax + b)^2 = -4ac - b^2 .........

[@alpcanakaydn6986]

@@Leeanne750 It works just fine,but my goal is to find other solutions in the question

[@angelofelisimolacruz1462]

@@Leeanne750 Thanks for this approach.

[@paulg444]

This guy is the man!!!.. Love his energy!

[@SandeepKumar-dw3sj]

Wow you have legend way to solve it

[@juancarlosquispemamani7238]

Genial!!! yo soy de Bolivia voy en la carrera de Ingeniería y voy aprendiendo mucho de ti... muchas gracias por compartir tus conocimientos!!!! sigue adelante!!! exitos!!!

[@nychan2939]

I love the completing square method since I was a child.

[@aamirakhtar5913]

We love your explanation 💘😻💜💛💚🧡 . Can you please tell us how you explain. When ever I try to explain any maths problem literally no one got it. You are awesome 👌

[@in-ty8vb]

I bet your explanation is good,they just don't know math

[@johnbiluke8406]

I like the Gatorade bottles in the background.

[@danieleferrara561]

Last one is the most interesting, thank you

[@sueyibaslanli3519]

Exactly, the third one

[@mathstutors9179]

7:35 What is the difference between “+or-“ and “-or+”

[@Crash-yp7ll]

If you have two or more of 'these' in eq, always use the top signs together or the bottom two signs together, but never the top and bottom of each together ...

[@stephenbeck7222]

No difference if you only have one of them in the equation. Sometimes we write, for example, the formulas for sum and difference for cosines with a +- on one side and a -+ on the other side to indicate when one side is adding then the other side is subtracting and vice versa.

[@Crash-yp7ll]

Agree ... - '/ ' always confusing - Doesn't totally mean '+ or -' but maybe better as '+ and -, one at a time, and in that order' ...

[@zerilioner639]

Hello, I have one math question:Find the equation of the tangent to the curve y =cos^2⁡ x when x=π/3 . Your solution should use radian measure. I kind of figured out m=-√3/2and y=1/4. Is the equation how to solve? Is it 1/4=√3/2(x-π/3)+y? Can you explain this question?

[@mokouf3]

3rd way is cleanest.

[@omograbi]

There was a forth way you mentioned in other vids where you reduced the equation in a table and then multiplied the contents of the table.

[@helloitsme3958]

hey bro i need help 1/a+a=b find 1/a^n+a^n in term b thanks

[@bhgtree]

"don't like fractions......when they see fractions 90% of them freak out." And thats only the teachers :)

[@MathNerd1729]

I just found out how the last way generalizes! It's quite fun! :) Start with: ax² + bx + c = 0 (c ≠ 0) Move the ax² term: bx + c = -ax² Multiply by 4c: 4bcx + 4c² = -4acx² Add b²x² and factor: b²x² + 4bcx + 4c² = (b² - 4ac)x² (bx + 2c)² = (b² - 4ac)x² Take the square root: bx + 2c = ± √(b² - 4ac) x Solve for x and rationalize the denominator to get the usual Quadratic Formula! :) Footnote: Apologies to BPRP about my previous comment; I meant the last way and didn't know how to tell you I made a typo! Additional note: The formula we get before rationalizing the denominator is known as the citardauq formula (That's quadratic backwards!)

[@willbishop1355]

I do really like the 3rd way, although as you said it won't always work.

[@professoraxolotl8960]

3:58 I'm a math teacher and the same thing happens to me quite a lot, I want to ask for something but I say the answer hahaha

[@wisdom6486]

& That's why I love Mathematics😍😍🤷😁😊😊

[@XAHMED5A]

prove that from L.H.S (secA.secB.cscA.cscB)/(cscA.cscB - secA.secB) = sec(A+B)

[@aryangupta7092]

Can u find the remainder when 17^(63) is divided by 1000

[@DownDance]

I like that you say with multiply everybody... Like these are humans

[@klausbuda7922]

I would use the quadratic equation to solve it

[@jimbobago]

But you need completing the square to develop the quadratic formula in the first place.

[@GDPlainA]

7:21 I cant unsee that -+ looking like a villager

[@GreenMeansGOF]

I disagree with method 3. Square root of x^2 is the absolute value when x is real. However, x is not necessarily real and is actually complex and non-real. I do not think sqrt(x^2)=+/-x is valid. I could be wrong, however. And yes, I acknowledge that you arrive at the correct answer but that does not mean that the method is valid.

[@MathNerd1729]

Well, the square roots of -x² could be ix or -ix. The principal root could be either one of these, yet because of the ±, both possibilities are covered! :)

[@arcader30]

4th way, use QUADRATIC FORMULA!! 😁😁

[@jimbobago]

But the only reason the quadratic formula exists is ... completing the square ... which is the point of the video.

[@qureshisiddig9274]

How amazing is that you keep superise me wow

[@thengodpbot7892]

Do you know general way to complete cube equation

[@blandon93]

Is there a way where one of x is equal to i or -i? I calculated one imaginary root which is close to -i (like -0,98i), I wonder if we ever can achieve whole i number.

[@flashthedash765]

The letter 'i'is basically an imaginary number since its not possible to solve the negative root. However if you write it as '-i' it'll simply cancels the negatives of root and the letter i and results in positive root

[@MohammadIbrahim-sq1xn]

=(x+i)(x+k) =x²+x(i+k)+ ik

[@Bonthefanfan]

#bprp, can u do 100 series, but this time is product summation.

[@BlessingIduh]

I prefer the third way

[@rikthecuber]

DO SOME DIFFERENTIAL EQNS BPRP!

[@blackpenredpen]

What's a differential equation? jk, here's the diff eq marathon: kzbin.info/www/bejne/m17Ghaydg8d4i6c

[@durgeshverma8131]

He means to use calculus method.

[@3r3nite98]

This is very cool.

[@pribato]

Are you from Singapore?

[@aweebthatlovesmath4220]

China

[@alinabilabdulghafoor1572]

Hello sir... can you help me solve this integration Show that ∫▒(x^4+1)/(x^2 √(x^4-1)) dx = √(x^4-1)/x +c

[@vinodgupta1776]

kzbin.info/www/bejne/fHrPlYWClKata6M

[@ayushhazarika6384]

There is another method known as midterm factorization...which is the easiest

[@DudsO_o]

although hating fractions, I prefer the first one

[@chocolateangel8743]

If you hate fractions, you should check out the fraction series that Dr. James Tanton has on his channel. He's a mathematics educator and researcher that's big on teaching the mathematical logic and concepts behind things. He believes that the more a student understands, the less he or she has to memorize. He deals with fractions differently than most people.

[@theophonchana5025]

sqrt (-x^(2)) = error

[@johndanielvillanueva8604]

Awesome

[@arirooz6240]

Oh the 🦒 is concentrated at class. It's so cute. This is a importand method about trinomious. TK

[@Amar-zw5md]

IIT Advance aspirants be like : We had few more ways left to solve that :)

[@crispyclips6268]

👍👍

[@Atreyaa499]

By simple quadratic formula 🤣😂😂🤣🤣

[@theophonchana5025]

sqrt (-9) = error

[@mpgopala]

In 2nd way, why multiply by 4a and not a? It would yield the same result with simpler arithmetic.

[@wafimarzouqmohammad8054]

In case the coefficient of x and x^2 are odd.

[@jimbobago]

What would it factor into?

[@kglmg93f]

-0,5 & 5,5

[@theophonchana5025]

sqrt (-36) = invalid input

[@m.arya_fr330]

10th ncert 4th chapter lol

[@juanpedro19840914]

Why do you (put) "plus or minus, cancel this out" rather than absolute value?

[@aweebthatlovesmath4220]

That's gonna ruine everything you don't know it's positive or negative so you put plus minus there's 2 solution. This is why: |2x-2|+2≠2x

[@juanpedro19840914]

@@aweebthatlovesmath4220. I know. What I'm saying is that instead of "plus or minus, cancel this out", he should have put absolute value.

[@lily_littleangel]

0th way: Wolfram Alpha

[@purim_sakamoto]

へええすごい いろんなやり方があるもんですね😀

[@saddude9574]

🐐👌

[@theophonchana5025]

x = invalid input

[@Leo-gb1mo]

3rd is quite interesting but too many steps

[@theophonchana5025]

x = error

[@psyrtemis1567]

People with a brain: Quadratic formula goes brrrr

[@fatinebadr7244]

thasn't simple to just use the delta , it's very fast that way

[@chitramc7238]

I solved this while looking at the thumbnail. It was taught in my 8th grade

[@sadeekmuhammad3646]

what's your name?

[@juniornembhard9513]

Simple stuff, I'm at a point where I just write down the answer no need to workout anything physically

[@orpattmaks490]

I got called stupid three ways ;-;

[@handle-4-19]

Formula method _ -b±✓b²-4ac/2a

[@carultch]

You'll get it wrong, if you forget the parenthesis.

[@handle-4-19]

@@carultch hmm

[@yummer7432]

There many ways, but they are the same in the core idea.

[@chimetimepaprika]

I am a complete square.

[@JohnSmith-rf1tx]

It's not that helpful to say that Method #3 doesn't work sometimes and then not explain why/how it does work and the reasons for when it won't.

[@EDT24930]

Man are you Taiwanese? just curious

[@Sanatan_saarthi_1729]

Question for today:what is inside the pokeball?😁😁

[@cameronspalding9792]

For the second method: why did we have to multiply by 8: couldn’t we have multiplied by 2

[@jimbobago]

When you multiply by 4 times the "a" term (8, in this example) you can factor the trinomial. In the general form, ax^2+bx+c=0 multiplying by 4a gives you 4a^2 x^2 + 4abx + 4ac = 0. Subtract 4ac from both sides and you get 4a^2 x^2 + 4abx = -4ac. Now you can add b^2 to both sides and the left side becomes 4a^2 x^2 + 4abx + b^2 which factors to (2ax + b)^2.

[@nxt8110]

Hãy dùng casio580vnx

[@theophonchana5025]

x = no answer

[@pulzewidth]

Holy fucking shit look at how fast my guy switches his markers! 1:23

[@robertveith6383]

Stop your major cursing, especially in a mathematics forum! It is ignorant and needless.

[@Moroccan_Buddy]

Are u indonesian

[@52.73]

公式解?

[@shravansrinivasan4982]

Type this: An amazing way to solve quadratic equation that has not gone viral

[@hamzashah4255]

2

[@vjlaxmanan6965]

Can u please get rid of ur ghoti :(

[@justacityboy4426]

Math is basically magic, but without all the magic

[@Exahax101]

It's logic not magic!

[@SofronPolitis]

That's why it's called mathemagics

[@Felixrizzlord]

@@Exahax101 yes

[@E12345E]

Given: Math is basically magic, but without all the magic Prove: Magic doesn’t exist math = magic Given math - magic = magic Given magic - magic = magic substitution POE 0 = magic Simplify this proves that magic does not exist

[@johnbiluke8406]

@@E12345E (YEAH, YOU IN THE CROWD, CAN YOU SPOT THE MISTAKE?)

[@SyberMath]

You have a way with Complex Numbers! Nice work!!! 🤩

[@blackpenredpen]

Thanks! 😃

[@SyberMath]

@@blackpenredpen My pleasure! 😊

[@vivekbhutada3049]

Hey syber! Big fan here!!

[@erikmensinga]

@marine dtadtfeld bruh no why

[@blackpenredpen]

Do you have a different way to complete the square for this equation?

[@ryancantpvp]

No because the video is still premiering lol!

[@purushothaman6698]

No

[@mathevengers1131]

Fourth method: Use quadratic formula Fifth way: Tell πkachu to use thunderbolt

[@beastgamer4932]

how do you use quadratic formula to complete the square

[@davidbrisbane7206]

We can set x = 1/y, as x = 0 is not a solution. So, 2x² + 6x + 9 = 0 is transformed into 9y² + 6y + 2 = 0 So, 36y² + 24y + 8 = 0 So, (6y + 2)² = -4 So, 6y + 2 = ±2i So, 3y = -1 ± i So, y = (-1 ± i)/3 So, x = 3/(-1 ± i) So x = (-3 ± 3i)/2

[@Firefly256]

Irrational Denominator to rational = rationalize Imaginary denominator to real = realize

[@blackpenredpen]

Try this cubic x^3-3x^2-3x-1=0 Hint: it's kinda similar to the 3rd way in this video. Solution: kzbin.info/www/bejne/gKuQi2Ogm9hljJY

[@crispyclips6268]

Bro can you please post some videos on calculus (majorly integral calculus) and functional equations too As I am preparing for jee advanced and the questions need practice for developing that approach. How to contact you ?

[@crispyclips6268]

And more questions like this one kzbin.info/www/bejne/aandk2B_pr53fM0

[@4ltrz555]

@@crispyclips6268 he has made a lot of integration speedruns and long runs. You can check it out in his playlists

[@crispyclips6268]

OK thanks

[@RazorM97]

At 5:45 i thought you were going to say, "let's delete that two and it will work out nicely". Man I was so wrong XD

[@electrocode4095]

There is one another method (How you can forget Shri Dharacharya's Formula 🤨) ax² + bx + c = 0 you can write x =( - b ⨦ √ (b² - 4*a*c) )/(2*a)

[@flashthedash765]

Also known as the quadratic formula

[@flashthedash765]

Apparently there are 3 ways

[@AliKhanMaths]

Well-remembered! But that's just a derivation of the conventional completing the square method, so I don't think it would count as another method of completing the square.

[@electrocode4095]

@Python Project Academy It can be able to make square just do some math for it i.e. after rearranging of variables and constant it would be (x+ b/2a)² = (b² - 4*a*c )/4*a²

[@jimbobago]

This formula is simply the generic result from using completing the square on ax^2 + bx + c = 0.

[@elias69420]

In fact, way #2 is the way people were doing it in India in the 11th century!

[@Songfugel]

2nd one felt most comfortable, since it was close to the normal way to solve it

[@tambuwalmathsclass]

I must try this in with my students

[@arshadalam]

Simply use quadratic formula

[@idrisShiningTimes]

I loved the first method honestly, since I'm basically used to solving fractions, and it gives out the answer in simplest form most of the time.

[@sakib5766]

3rd method: when u r too crazy for a perfect square

[@win.diesal]

Sir please explain in hindi language

[@carultch]

I don't think he speaks Hindi.

[@eipimath]

Thanks for sharing! I posted a video on completing the square using remainder theorem. Hope to get your opinion on it.

[@kcfish4862]

Yooo I didn't even know you are Taiwanese, you watching Olympics?

[@nory2441]

Hey bprp love from India nice videos can you plz make 100 limits in 1 take plz I commented before but u din't see

[@willie333b]

Just use the formula lol

[@princemoipolai7366]

The first Asian guy to grow this much man beard

[@patrickpablo217]

Nice! All three were great :) I'll add another twist that can fit with any of the three. Recently I switched from "completing the square" to "completing the difference of squares" and I like it a lot more. I'll give a basic example: x^2+6x+8=0 proceed as usual but *don't* move anything to the RHS: x^2 + 6x + 3^2 + -(3)^2 + 8 = 0 (x + 3)^2 - ( 3^2 - 8 ) = 0 that second term isn't a square yet but we can write it as one easily: (x + 3)^2 - (√[ 3^2 - 8 ])^2 = 0 Now we have a difference of squares, but let's simplify first: (x + 3)^2 - (√[ 9 - 8 ])^2 = 0 (x + 3)^2 - (√[ 1 ])^2 = 0 (x + 3)^2 - (1)^2 = 0 now difference of squares takes care of the ± automatically and gives (x+3+1)*(x+3-1)=0 (x+4)*(x+2)=0 so x={2,4} I really like this method since you never have to deal with moving things from LHS to RHS or back, and it's more like factoring, and it avoids the ± issue completely. It also has direct relation to the parabola associated with the quadratic: the first of the squares gives the line of symmetry (the x-coordinate of the vertex), and the second one provides the distance to the solutions and the y-coordinate of the vertex. And it saves steps, which is nice.

[@patrickpablo217]

for this equation 2*x^2 + 6x + 9=0: (doing more arithmetic than necessary, just to not get people lost) 2*x^2+6x+(3/√2)^2 -(3/√2)^2 + 9 =0 (√2*x+(3/√2))^2 - ((3/√2)^2 - 9) = 0 (√2*x+(3/√2))^2 - (9/2 - 9) = 0 (√2*x+(3/√2))^2 - (-9/2) = 0 (√2*x+(3/√2))^2 - (i*3/√2)^2 = 0 [so here next is where we use difference of squares (x^2 - y^2) = (x+y)*(x-y)] ( √2*x+(3/√2) + i*3/√2 ) * ( √2*x+(3/√2) - i*3/√2 ) = 0 [group the constant terms:] (√2*x + (3+i*3)/√2)*(√2*x + (3-i*3)/√2)=0 [you could be done here if you know that if (mx+n)=0 then x must equal -n/m, but if not, pull out a √2 from each factor:] √2*(x+(3+i*3)/2) * √2*(x+(3-i*3)/2)=0 [combine them:] 2*(x+(3+i*3)/2)*(x+(3-i*3)/2)=0 Then we just read off the solutions as normal: x={ -3/2 -(3/2)*i, -3/2+(3/2)*i } which are the same as in the video