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Simplifying 31x(x + 4) = 9920 Reorder the terms: 31x(4 + x) = 9920 (4 * 31x + x * 31x) = 9920 (124x + 31x2) = 9920 Solving 124x + 31x2 = 9920 Solving for variable 'x'. Reorder the terms: -9920 + 124x + 31x2 = 9920 + -9920 Combine like terms: 9920 + -9920 = 0 -9920 + 124x + 31x2 = 0 Factor out the Greatest Common Factor (GCF), '31'. 31(-320 + 4x + x2) = 0 Factor a trinomial. 31((-20 + -1x)(16 + -1x)) = 0 Ignore the factor 31.Subproblem 1
Set the factor '(-20 + -1x)' equal to zero and attempt to solve: Simplifying -20 + -1x = 0 Solving -20 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + -1x = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -1x = 0 + 20 -1x = 0 + 20 Combine like terms: 0 + 20 = 20 -1x = 20 Divide each side by '-1'. x = -20 Simplifying x = -20Subproblem 2
Set the factor '(16 + -1x)' equal to zero and attempt to solve: Simplifying 16 + -1x = 0 Solving 16 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + -1x = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -1x = 0 + -16 -1x = 0 + -16 Combine like terms: 0 + -16 = -16 -1x = -16 Divide each side by '-1'. x = 16 Simplifying x = 16Solution
x = {-20, 16}
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