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Simplifying x + (x + -4) + 2x + (x2 + -20) + (x + 32) = 112 Reorder the terms: x + (-4 + x) + 2x + (x2 + -20) + (x + 32) = 112 Remove parenthesis around (-4 + x) x + -4 + x + 2x + (x2 + -20) + (x + 32) = 112 Reorder the terms: x + -4 + x + 2x + (-20 + x2) + (x + 32) = 112 Remove parenthesis around (-20 + x2) x + -4 + x + 2x + -20 + x2 + (x + 32) = 112 Reorder the terms: x + -4 + x + 2x + -20 + x2 + (32 + x) = 112 Remove parenthesis around (32 + x) x + -4 + x + 2x + -20 + x2 + 32 + x = 112 Reorder the terms: -4 + -20 + 32 + x + x + 2x + x + x2 = 112 Combine like terms: -4 + -20 = -24 -24 + 32 + x + x + 2x + x + x2 = 112 Combine like terms: -24 + 32 = 8 8 + x + x + 2x + x + x2 = 112 Combine like terms: x + x = 2x 8 + 2x + 2x + x + x2 = 112 Combine like terms: 2x + 2x = 4x 8 + 4x + x + x2 = 112 Combine like terms: 4x + x = 5x 8 + 5x + x2 = 112 Solving 8 + 5x + x2 = 112 Solving for variable 'x'. Reorder the terms: 8 + -112 + 5x + x2 = 112 + -112 Combine like terms: 8 + -112 = -104 -104 + 5x + x2 = 112 + -112 Combine like terms: 112 + -112 = 0 -104 + 5x + x2 = 0 Factor a trinomial. (-13 + -1x)(8 + -1x) = 0Subproblem 1
Set the factor '(-13 + -1x)' equal to zero and attempt to solve: Simplifying -13 + -1x = 0 Solving -13 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + -1x = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -1x = 0 + 13 -1x = 0 + 13 Combine like terms: 0 + 13 = 13 -1x = 13 Divide each side by '-1'. x = -13 Simplifying x = -13Subproblem 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 = {-13, 8}
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