Identity Equation

Algebra Level 1

Given that x x is a real number such that x 2 − 4 x + 4 = 0 x^2-4x+4=0 , find the value of x x .

4 2 6 8

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David Zhang by david zhang , 20, China

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15 solutions

Victor Loh
Jan 29, 2015

x 2 − 4 x + 4 = 0 ⟹ ( x − 2 ) 2 = 0 ⟹ x − 2 = 0 ⟹ x = 2 x^2-4x+4=0 \implies (x-2)^2=0 \implies x-2=0 \implies x=\boxed{2} .

192 Helpful 21 Interesting 28 Brilliant 51 Confused

Nope. Don't see it.

Dylan Golden - 3 years, 6 months ago

It is a quadratic so shouldn't it have two answers.

Shane Coe - 3 years, 4 months ago

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They are two but identical.

Al-Hamza Omar - 1 year ago

Yes, but the square root evaluates to 0, which is the only number where posiitive/negative doesn't matter. Therefore there's only one answer

Art InLines - 1 month, 2 weeks ago

if you speak to a person that never did math you really think that they would figure it out like that you should make more easier don't you think

Judith Ortiz - 1 year, 2 months ago

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it is easy go read the wiki that's next to answer button after 1 hr ull see how helpful that was

Tucan 444 - 11 months ago

Another solution is the square root of 4.

Jakob Vlietstra - 5 years, 3 months ago

So 2^2-4x2+4=0? 2x2=4 4×2=8 4-8=-4+4=0 Quit making it sound harder and use the plug in method

Justin Allen - 5 years, 6 months ago

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Justin Allen

What if they didn't have the 4 choices? Using the plug-in method for problems wouldn't really get you better at math, unless you want to be better at using plug-in method

Alan Chen - 5 years, 5 months ago
Justin Cruta
Feb 7, 2015


Many solutions can be used! It can be by factoring such that
x^{2}-4x+4=0 is (x-2)(x-2)=0 and x=2
or use the quadratic form:


61 Helpful 3 Interesting 3 Brilliant 7 Confused

I used that method

Harvey Smith - 5 years, 1 month ago

I did just that in my Brain;)

Jan Grünwaldt - 5 years, 5 months ago

Can't lose with the old Quadratic formula.

Gerald Dixon John Cummings - 4 years, 7 months ago

Or complete the square much simpler

Raviv Talkar - 3 years, 1 month ago
Suhail Ahmed
Feb 5, 2015

x^2-4x+4 =0

x^2-2x-2x+4=0

x(x-2) -2(x-2)=0

(x-2) (x-2)=0

(x-2)^2=0

x=2

26 Helpful 4 Interesting 5 Brilliant 9 Confused

All will lead to same and.

prabhat singh - 4 years, 10 months ago
Bob Gelber
Nov 12, 2015

2X2-4X2=4=0

10 Helpful 0 Interesting 0 Brilliant 4 Confused
Hussein Kiki
Jan 30, 2015

5 Helpful 0 Interesting 0 Brilliant 2 Confused
Cianuck Manuel
Mar 1, 2016

The correct answer is -2 not 2 ... But it's ok

3 Helpful 1 Interesting 0 Brilliant 0 Confused

Only positive 2 works. I believe you lost track of a negative sign (easy mistake to make 🤔).

Carla Maldonado - 2 years, 8 months ago

Try to put it in equation!!

candy blocs - 1 year ago
Beau Clemmons
Jan 3, 2016

x^2 - 4x + 4 = 0 x^2 - 4x = -4 Plug in and solve for x to balance the equation with -4. 2 is the only solution that now clearly works. 2^2 -4(2)=-4.

1 Helpful 0 Interesting 1 Brilliant 1 Confused

x = 2 is one of two solutions. The other one is x= -2.

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Wrong, x = 2 is both solutions to this problem.

b^2 - 4 a c = 16 - 4 -4 = 0 [-(b) +- 0]/2 a = -(-4)/2 = 2. Sp, x' = x" = 2, Q.E.D.

Thiago Medeiros - 5 years, 7 months ago

It cannot be -2 as if x=-2 then the equation would have been x^2-4x+4=16

James Butler - 5 years, 6 months ago

Differentiate the equation for 'x' on both sides, will get x=2

2 Helpful 0 Interesting 0 Brilliant 0 Confused

This solution is wrong, it is an equation, you should never differentiate an equation. For example: differentiate x = 5 x = 5 gives 1 = 0 1 = 0 which is absurd.

Pi Han Goh - 6 years, 2 months ago

As has been said, you don't differentiate equations, you differentiate functions. This is the former.

Alex Thies - 5 years, 9 months ago
Zenobia Roy
Aug 12, 2019

since (a-b)^2=a^2+b^2-2ab

if you look carefully, you can easily find that the equation above is just as same as the formula above.

x^2+2^2-2 *2 x=(x-2)^2

then x would be 2.

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Tomer Horowitz
Feb 14, 2019

Based on x 2 − x ( p − q ) + p q = ( x + p ) ( x − q ) x^2 - x(p-q) + pq = (x+p)(x-q)

we can rearrange the equation

x 2 − 4 x + 4 = ( x + 2 ) ( x − 2 ) x^2 - 4x + 4 = (x+2)(x-2)

and deduce the question to

2 − x = 0 2-x = 0 which is x = 2 x = 2

so that we end with a multiplication of 0. ( 2 + 2 ) ( 2 − 2 ) = ( 4 ) ( 0 ) = 0 (2+2)(2-2) = (4)(0) = 0

0 Helpful 1 Interesting 0 Brilliant 1 Confused
Annie Li
Mar 20, 2017

Trial and error is the best way to do this because this is a multiple choice question with only four choices.

1 Helpful 0 Interesting 1 Brilliant 1 Confused
George Dickson
Dec 1, 2015

(X-2)^2 -(-2)^2 +4 (X-2)^2 (X-2)=0 =2

1 Helpful 0 Interesting 0 Brilliant 1 Confused
Tom Wang
Jun 25, 2020

x 2 − 4 x + 4 = ( x − 2 ) 2 x^2-4x+4=(x-2)^2 , and setting this equal to 0 gives x = 2 x=2

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Andy Shi
Feb 18, 2018

\(\frac{w}4 ||/lm :nkl nkoh

||

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0 Helpful 0 Interesting 0 Brilliant 1 Confused

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