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# (x-1)^2 = (x-2)^2

Solve for x.  I know you have to extract the roots, but I'm not sure about the +/-

### 3 Answers by Expert Tutors

Kirill Z. | Physics, math tutor with great knowledge and teaching skillsPhysics, math tutor with great knowledge...
4.9 4.9 (174 lesson ratings) (174)
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There are two possibilities:
x-1=x-2
x-1=2-x

First equation does not have any solutions. Second one gives x=3/2.

Or you can expand both sides.
x2-2x+1=x2-4x+4
From this you will get, by moving numbers to the right, and x-containing terms to the left:
x2-2x-x2+4x=4-1
2x=3
x=3/2

Thank you! :)
You're welcome any time!
Parviz F. | Mathematics professor at Community CollegesMathematics professor at Community Colle...
4.8 4.8 (4 lesson ratings) (4)
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( x-1) ^2 = ( x-2) ^2

Take the square root of both sides:       If you expand both sides:

X - 1 = + ( X-2) , no answer               X^2 -2X + 1 = X^2 -4x +4

X -1 = - ( x-2)                                  -2x + 4X  = 4 - 1

x -1 = -x +2                                    2X = 3

2X = 3                                              X = 3/2

X = 3/2
George T. | George T.--"It's All About Math!"George T.--"It's All About Math!"
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Nisya:

The first thing I would do is "unravel" the factored expressions on each side of the equation, by multiplying out each side, as follows:

(x-1)2=(x-2)2
x2-2x+1=x2-4x+4

Next (by subtracting) I would bring all the terms with x to the left side and all non-x terms to the right side as follows:

x2-x2  -2x+4x  =  4-1
0     +   2x     =    3
2x     =    3

Finally solve for x, by dividing both sides by 2 to get:

x=3/2

You can check you work, by plugging 3/2 in for the value of x in the original expression:

(x-1)2=(x-2)2
(3/2-1)2=(3/2-2)2
(3/2-2/2)2=(3/2-4/2)2
(1/2)2=(-1/2)2
1/4=1/4 (check!)

Goo Luck!

George