(x-2)*(x-2)-(3-x)*(3-x)=1

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Solution for (x-2)*(x-2)-(3-x)*(3-x)=1 equation: 


Simplifying
(x + -2)(x + -2) + -1(3 + -1x)(3 + -1x) = 1

Reorder the terms:
(-2 + x)(x + -2) + -1(3 + -1x)(3 + -1x) = 1

Reorder the terms:
(-2 + x)(-2 + x) + -1(3 + -1x)(3 + -1x) = 1

Multiply (-2 + x) * (-2 + x)
(-2(-2 + x) + x(-2 + x)) + -1(3 + -1x)(3 + -1x) = 1
((-2 * -2 + x * -2) + x(-2 + x)) + -1(3 + -1x)(3 + -1x) = 1
((4 + -2x) + x(-2 + x)) + -1(3 + -1x)(3 + -1x) = 1
(4 + -2x + (-2 * x + x * x)) + -1(3 + -1x)(3 + -1x) = 1
(4 + -2x + (-2x + x2)) + -1(3 + -1x)(3 + -1x) = 1

Combine like terms: -2x + -2x = -4x
(4 + -4x + x2) + -1(3 + -1x)(3 + -1x) = 1

Multiply (3 + -1x) * (3 + -1x)
4 + -4x + x2 + -1(3(3 + -1x) + -1x * (3 + -1x)) = 1
4 + -4x + x2 + -1((3 * 3 + -1x * 3) + -1x * (3 + -1x)) = 1
4 + -4x + x2 + -1((9 + -3x) + -1x * (3 + -1x)) = 1
4 + -4x + x2 + -1(9 + -3x + (3 * -1x + -1x * -1x)) = 1
4 + -4x + x2 + -1(9 + -3x + (-3x + 1x2)) = 1

Combine like terms: -3x + -3x = -6x
4 + -4x + x2 + -1(9 + -6x + 1x2) = 1
4 + -4x + x2 + (9 * -1 + -6x * -1 + 1x2 * -1) = 1
4 + -4x + x2 + (-9 + 6x + -1x2) = 1

Reorder the terms:
4 + -9 + -4x + 6x + x2 + -1x2 = 1

Combine like terms: 4 + -9 = -5
-5 + -4x + 6x + x2 + -1x2 = 1

Combine like terms: -4x + 6x = 2x
-5 + 2x + x2 + -1x2 = 1

Combine like terms: x2 + -1x2 = 0
-5 + 2x + 0 = 1
-5 + 2x = 1

Solving
-5 + 2x = 1

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '5' to each side of the equation.
-5 + 5 + 2x = 1 + 5

Combine like terms: -5 + 5 = 0
0 + 2x = 1 + 5
2x = 1 + 5

Combine like terms: 1 + 5 = 6
2x = 6

Divide each side by '2'.
x = 3

Simplifying
x = 3

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