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

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

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# 3 Answers

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.

x

^{2}-2x+1=x^{2}-4x+4From this you will get, by moving numbers to the right, and x-containing terms to the left:

x

^{2}-2x-x^{2}+4x=4-12x=3

x=3/2

( 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

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}**x**

^{2}-2x+1=x^{2}-4x+4Next (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:

**x**

^{2}-x^{2}-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

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