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Simplifying -32x = 2x2 + -1x + -51 Reorder the terms: -32x = -51 + -1x + 2x2 Solving -32x = -51 + -1x + 2x2 Solving for variable 'x'. Reorder the terms: 51 + -32x + x + -2x2 = -51 + -1x + 2x2 + 51 + x + -2x2 Combine like terms: -32x + x = -31x 51 + -31x + -2x2 = -51 + -1x + 2x2 + 51 + x + -2x2 Reorder the terms: 51 + -31x + -2x2 = -51 + 51 + -1x + x + 2x2 + -2x2 Combine like terms: -51 + 51 = 0 51 + -31x + -2x2 = 0 + -1x + x + 2x2 + -2x2 51 + -31x + -2x2 = -1x + x + 2x2 + -2x2 Combine like terms: -1x + x = 0 51 + -31x + -2x2 = 0 + 2x2 + -2x2 51 + -31x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 51 + -31x + -2x2 = 0 Factor a trinomial. (3 + -2x)(17 + x) = 0Subproblem 1
Set the factor '(3 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Divide each side by '-2'. x = 1.5 Simplifying x = 1.5Subproblem 2
Set the factor '(17 + x)' equal to zero and attempt to solve: Simplifying 17 + x = 0 Solving 17 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + x = 0 + -17 Combine like terms: 17 + -17 = 0 0 + x = 0 + -17 x = 0 + -17 Combine like terms: 0 + -17 = -17 x = -17 Simplifying x = -17Solution
x = {1.5, -17}
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