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Simplifying 31x(x + 4) = 4340 Reorder the terms: 31x(4 + x) = 4340 (4 * 31x + x * 31x) = 4340 (124x + 31x2) = 4340 Solving 124x + 31x2 = 4340 Solving for variable 'x'. Reorder the terms: -4340 + 124x + 31x2 = 4340 + -4340 Combine like terms: 4340 + -4340 = 0 -4340 + 124x + 31x2 = 0 Factor out the Greatest Common Factor (GCF), '31'. 31(-140 + 4x + x2) = 0 Factor a trinomial. 31((-14 + -1x)(10 + -1x)) = 0 Ignore the factor 31.Subproblem 1
Set the factor '(-14 + -1x)' equal to zero and attempt to solve: Simplifying -14 + -1x = 0 Solving -14 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + -1x = 0 + 14 Combine like terms: -14 + 14 = 0 0 + -1x = 0 + 14 -1x = 0 + 14 Combine like terms: 0 + 14 = 14 -1x = 14 Divide each side by '-1'. x = -14 Simplifying x = -14Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve: Simplifying 10 + -1x = 0 Solving 10 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1x = 0 + -10 -1x = 0 + -10 Combine like terms: 0 + -10 = -10 -1x = -10 Divide each side by '-1'. x = 10 Simplifying x = 10Solution
x = {-14, 10}
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