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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There are two possibilities:
First equation does not have any solutions. Second one gives x=3/2.
Or you can expand both sides.
From this you will get, by moving numbers to the right, and x-containing terms to the left:
( 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
The first thing I would do is "unravel" the factored expressions on each side of the equation, by multiplying out each side, as follows:
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:
You can check you work, by plugging 3/2 in for the value of x in the original expression: