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Simplifying -2x2 + 120x + -788 = 500 Reorder the terms: -788 + 120x + -2x2 = 500 Solving -788 + 120x + -2x2 = 500 Solving for variable 'x'. Reorder the terms: -788 + -500 + 120x + -2x2 = 500 + -500 Combine like terms: -788 + -500 = -1288 -1288 + 120x + -2x2 = 500 + -500 Combine like terms: 500 + -500 = 0 -1288 + 120x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-644 + 60x + -1x2) = 0 Factor a trinomial. 2((-46 + x)(14 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-46 + x)' equal to zero and attempt to solve: Simplifying -46 + x = 0 Solving -46 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '46' to each side of the equation. -46 + 46 + x = 0 + 46 Combine like terms: -46 + 46 = 0 0 + x = 0 + 46 x = 0 + 46 Combine like terms: 0 + 46 = 46 x = 46 Simplifying x = 46Subproblem 2
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 = 14Solution
x = {46, 14}
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