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Simplifying (x + 8)(x + -7) = x + 8 Reorder the terms: (8 + x)(x + -7) = x + 8 Reorder the terms: (8 + x)(-7 + x) = x + 8 Multiply (8 + x) * (-7 + x) (8(-7 + x) + x(-7 + x)) = x + 8 ((-7 * 8 + x * 8) + x(-7 + x)) = x + 8 ((-56 + 8x) + x(-7 + x)) = x + 8 (-56 + 8x + (-7 * x + x * x)) = x + 8 (-56 + 8x + (-7x + x2)) = x + 8 Combine like terms: 8x + -7x = 1x (-56 + 1x + x2) = x + 8 Reorder the terms: -56 + 1x + x2 = 8 + x Solving -56 + 1x + x2 = 8 + x Solving for variable 'x'. Reorder the terms: -56 + -8 + 1x + -1x + x2 = 8 + x + -8 + -1x Combine like terms: -56 + -8 = -64 -64 + 1x + -1x + x2 = 8 + x + -8 + -1x Combine like terms: 1x + -1x = 0 -64 + 0 + x2 = 8 + x + -8 + -1x -64 + x2 = 8 + x + -8 + -1x Reorder the terms: -64 + x2 = 8 + -8 + x + -1x Combine like terms: 8 + -8 = 0 -64 + x2 = 0 + x + -1x -64 + x2 = x + -1x Combine like terms: x + -1x = 0 -64 + x2 = 0 Factor a difference between two squares. (8 + x)(-8 + x) = 0Subproblem 1
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 = -8Subproblem 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 = {-8, 8}
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