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Simplifying x(30 + -2x) = 112 (30 * x + -2x * x) = 112 (30x + -2x2) = 112 Solving 30x + -2x2 = 112 Solving for variable 'x'. Reorder the terms: -112 + 30x + -2x2 = 112 + -112 Combine like terms: 112 + -112 = 0 -112 + 30x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-56 + 15x + -1x2) = 0 Factor a trinomial. 2((-8 + x)(7 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-8 + x)' equal to zero and attempt to solve: Simplifying -8 + x = 0 Solving -8 + x = 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 + x = 0 + 8 Combine like terms: -8 + 8 = 0 0 + x = 0 + 8 x = 0 + 8 Combine like terms: 0 + 8 = 8 x = 8 Simplifying x = 8Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 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 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Divide each side by '-1'. x = 7 Simplifying x = 7Solution
x = {8, 7}
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