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Simplifying x2 + (x + -2)(x + -2) = (x + 2)(x + 2) Reorder the terms: x2 + (-2 + x)(x + -2) = (x + 2)(x + 2) Reorder the terms: x2 + (-2 + x)(-2 + x) = (x + 2)(x + 2) Multiply (-2 + x) * (-2 + x) x2 + (-2(-2 + x) + x(-2 + x)) = (x + 2)(x + 2) x2 + ((-2 * -2 + x * -2) + x(-2 + x)) = (x + 2)(x + 2) x2 + ((4 + -2x) + x(-2 + x)) = (x + 2)(x + 2) x2 + (4 + -2x + (-2 * x + x * x)) = (x + 2)(x + 2) x2 + (4 + -2x + (-2x + x2)) = (x + 2)(x + 2) Combine like terms: -2x + -2x = -4x x2 + (4 + -4x + x2) = (x + 2)(x + 2) Reorder the terms: 4 + -4x + x2 + x2 = (x + 2)(x + 2) Combine like terms: x2 + x2 = 2x2 4 + -4x + 2x2 = (x + 2)(x + 2) Reorder the terms: 4 + -4x + 2x2 = (2 + x)(x + 2) Reorder the terms: 4 + -4x + 2x2 = (2 + x)(2 + x) Multiply (2 + x) * (2 + x) 4 + -4x + 2x2 = (2(2 + x) + x(2 + x)) 4 + -4x + 2x2 = ((2 * 2 + x * 2) + x(2 + x)) 4 + -4x + 2x2 = ((4 + 2x) + x(2 + x)) 4 + -4x + 2x2 = (4 + 2x + (2 * x + x * x)) 4 + -4x + 2x2 = (4 + 2x + (2x + x2)) Combine like terms: 2x + 2x = 4x 4 + -4x + 2x2 = (4 + 4x + x2) Add '-4' to each side of the equation. 4 + -4x + -4 + 2x2 = 4 + 4x + -4 + x2 Reorder the terms: 4 + -4 + -4x + 2x2 = 4 + 4x + -4 + x2 Combine like terms: 4 + -4 = 0 0 + -4x + 2x2 = 4 + 4x + -4 + x2 -4x + 2x2 = 4 + 4x + -4 + x2 Reorder the terms: -4x + 2x2 = 4 + -4 + 4x + x2 Combine like terms: 4 + -4 = 0 -4x + 2x2 = 0 + 4x + x2 -4x + 2x2 = 4x + x2 Solving -4x + 2x2 = 4x + x2 Solving for variable 'x'. Reorder the terms: -4x + -4x + 2x2 + -1x2 = 4x + x2 + -4x + -1x2 Combine like terms: -4x + -4x = -8x -8x + 2x2 + -1x2 = 4x + x2 + -4x + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 -8x + 1x2 = 4x + x2 + -4x + -1x2 Reorder the terms: -8x + 1x2 = 4x + -4x + x2 + -1x2 Combine like terms: 4x + -4x = 0 -8x + 1x2 = 0 + x2 + -1x2 -8x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -8x + 1x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-8 + x) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-8 + x)' equal to zero and attempt to solve: Simplifying -8 + x = 0 Solving -8 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 0 + 8 Combine like terms: -8 + 8 = 0 0 + x = 0 + 8 x = 0 + 8 Combine like terms: 0 + 8 = 8 x = 8 Simplifying x = 8Solution
x = {0, 8}
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