(x-2)*(x-2)+(x-9)*(x-9)=(x-11)*(x-11)

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Solution for (x-2)*(x-2)+(x-9)*(x-9)=(x-11)*(x-11) equation:


Simplifying
(x + -2)(x + -2) + (x + -9)(x + -9) = (x + -11)(x + -11)

Reorder the terms:
(-2 + x)(x + -2) + (x + -9)(x + -9) = (x + -11)(x + -11)

Reorder the terms:
(-2 + x)(-2 + x) + (x + -9)(x + -9) = (x + -11)(x + -11)

Multiply (-2 + x) * (-2 + x)
(-2(-2 + x) + x(-2 + x)) + (x + -9)(x + -9) = (x + -11)(x + -11)
((-2 * -2 + x * -2) + x(-2 + x)) + (x + -9)(x + -9) = (x + -11)(x + -11)
((4 + -2x) + x(-2 + x)) + (x + -9)(x + -9) = (x + -11)(x + -11)
(4 + -2x + (-2 * x + x * x)) + (x + -9)(x + -9) = (x + -11)(x + -11)
(4 + -2x + (-2x + x2)) + (x + -9)(x + -9) = (x + -11)(x + -11)

Combine like terms: -2x + -2x = -4x
(4 + -4x + x2) + (x + -9)(x + -9) = (x + -11)(x + -11)

Reorder the terms:
4 + -4x + x2 + (-9 + x)(x + -9) = (x + -11)(x + -11)

Reorder the terms:
4 + -4x + x2 + (-9 + x)(-9 + x) = (x + -11)(x + -11)

Multiply (-9 + x) * (-9 + x)
4 + -4x + x2 + (-9(-9 + x) + x(-9 + x)) = (x + -11)(x + -11)
4 + -4x + x2 + ((-9 * -9 + x * -9) + x(-9 + x)) = (x + -11)(x + -11)
4 + -4x + x2 + ((81 + -9x) + x(-9 + x)) = (x + -11)(x + -11)
4 + -4x + x2 + (81 + -9x + (-9 * x + x * x)) = (x + -11)(x + -11)
4 + -4x + x2 + (81 + -9x + (-9x + x2)) = (x + -11)(x + -11)

Combine like terms: -9x + -9x = -18x
4 + -4x + x2 + (81 + -18x + x2) = (x + -11)(x + -11)

Reorder the terms:
4 + 81 + -4x + -18x + x2 + x2 = (x + -11)(x + -11)

Combine like terms: 4 + 81 = 85
85 + -4x + -18x + x2 + x2 = (x + -11)(x + -11)

Combine like terms: -4x + -18x = -22x
85 + -22x + x2 + x2 = (x + -11)(x + -11)

Combine like terms: x2 + x2 = 2x2
85 + -22x + 2x2 = (x + -11)(x + -11)

Reorder the terms:
85 + -22x + 2x2 = (-11 + x)(x + -11)

Reorder the terms:
85 + -22x + 2x2 = (-11 + x)(-11 + x)

Multiply (-11 + x) * (-11 + x)
85 + -22x + 2x2 = (-11(-11 + x) + x(-11 + x))
85 + -22x + 2x2 = ((-11 * -11 + x * -11) + x(-11 + x))
85 + -22x + 2x2 = ((121 + -11x) + x(-11 + x))
85 + -22x + 2x2 = (121 + -11x + (-11 * x + x * x))
85 + -22x + 2x2 = (121 + -11x + (-11x + x2))

Combine like terms: -11x + -11x = -22x
85 + -22x + 2x2 = (121 + -22x + x2)

Add '22x' to each side of the equation.
85 + -22x + 22x + 2x2 = 121 + -22x + 22x + x2

Combine like terms: -22x + 22x = 0
85 + 0 + 2x2 = 121 + -22x + 22x + x2
85 + 2x2 = 121 + -22x + 22x + x2

Combine like terms: -22x + 22x = 0
85 + 2x2 = 121 + 0 + x2
85 + 2x2 = 121 + x2

Solving
85 + 2x2 = 121 + x2

Solving for variable 'x'.

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

Add '-1x2' to each side of the equation.
85 + 2x2 + -1x2 = 121 + x2 + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
85 + 1x2 = 121 + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
85 + 1x2 = 121 + 0
85 + 1x2 = 121

Add '-85' to each side of the equation.
85 + -85 + 1x2 = 121 + -85

Combine like terms: 85 + -85 = 0
0 + 1x2 = 121 + -85
1x2 = 121 + -85

Combine like terms: 121 + -85 = 36
1x2 = 36

Divide each side by '1'.
x2 = 36

Simplifying
x2 = 36

Take the square root of each side:
x = {-6, 6}

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