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Simplifying x + -4 = x2 + 13x + 31 Reorder the terms: -4 + x = x2 + 13x + 31 Reorder the terms: -4 + x = 31 + 13x + x2 Solving -4 + x = 31 + 13x + x2 Solving for variable 'x'. Reorder the terms: -4 + -31 + x + -13x + -1x2 = 31 + 13x + x2 + -31 + -13x + -1x2 Combine like terms: -4 + -31 = -35 -35 + x + -13x + -1x2 = 31 + 13x + x2 + -31 + -13x + -1x2 Combine like terms: x + -13x = -12x -35 + -12x + -1x2 = 31 + 13x + x2 + -31 + -13x + -1x2 Reorder the terms: -35 + -12x + -1x2 = 31 + -31 + 13x + -13x + x2 + -1x2 Combine like terms: 31 + -31 = 0 -35 + -12x + -1x2 = 0 + 13x + -13x + x2 + -1x2 -35 + -12x + -1x2 = 13x + -13x + x2 + -1x2 Combine like terms: 13x + -13x = 0 -35 + -12x + -1x2 = 0 + x2 + -1x2 -35 + -12x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -35 + -12x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(35 + 12x + x2) = 0 Factor a trinomial. -1((7 + x)(5 + x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(7 + x)' equal to zero and attempt to solve: Simplifying 7 + x = 0 Solving 7 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + x = 0 + -7 x = 0 + -7 Combine like terms: 0 + -7 = -7 x = -7 Simplifying x = -7Subproblem 2
Set the factor '(5 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Simplifying x = -5Solution
x = {-7, -5}
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