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Simplifying (x + 8)(x + -7) = 16 Reorder the terms: (8 + x)(x + -7) = 16 Reorder the terms: (8 + x)(-7 + x) = 16 Multiply (8 + x) * (-7 + x) (8(-7 + x) + x(-7 + x)) = 16 ((-7 * 8 + x * 8) + x(-7 + x)) = 16 ((-56 + 8x) + x(-7 + x)) = 16 (-56 + 8x + (-7 * x + x * x)) = 16 (-56 + 8x + (-7x + x2)) = 16 Combine like terms: 8x + -7x = 1x (-56 + 1x + x2) = 16 Solving -56 + 1x + x2 = 16 Solving for variable 'x'. Reorder the terms: -56 + -16 + 1x + x2 = 16 + -16 Combine like terms: -56 + -16 = -72 -72 + 1x + x2 = 16 + -16 Combine like terms: 16 + -16 = 0 -72 + 1x + x2 = 0 Factor a trinomial. (-9 + -1x)(8 + -1x) = 0Subproblem 1
Set the factor '(-9 + -1x)' equal to zero and attempt to solve: Simplifying -9 + -1x = 0 Solving -9 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -1x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1x = 0 + 9 -1x = 0 + 9 Combine like terms: 0 + 9 = 9 -1x = 9 Divide each side by '-1'. x = -9 Simplifying x = -9Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve: Simplifying 8 + -1x = 0 Solving 8 + -1x = 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 + -1x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1x = 0 + -8 -1x = 0 + -8 Combine like terms: 0 + -8 = -8 -1x = -8 Divide each side by '-1'. x = 8 Simplifying x = 8Solution
x = {-9, 8}
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