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