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Simplifying 2x2 + 12x + -13 = 257 Reorder the terms: -13 + 12x + 2x2 = 257 Solving -13 + 12x + 2x2 = 257 Solving for variable 'x'. Reorder the terms: -13 + -257 + 12x + 2x2 = 257 + -257 Combine like terms: -13 + -257 = -270 -270 + 12x + 2x2 = 257 + -257 Combine like terms: 257 + -257 = 0 -270 + 12x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-135 + 6x + x2) = 0 Factor a trinomial. 2((-15 + -1x)(9 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-15 + -1x)' equal to zero and attempt to solve: Simplifying -15 + -1x = 0 Solving -15 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + -1x = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -1x = 0 + 15 -1x = 0 + 15 Combine like terms: 0 + 15 = 15 -1x = 15 Divide each side by '-1'. x = -15 Simplifying x = -15Subproblem 2
Set the factor '(9 + -1x)' equal to zero and attempt to solve: Simplifying 9 + -1x = 0 Solving 9 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1x = 0 + -9 -1x = 0 + -9 Combine like terms: 0 + -9 = -9 -1x = -9 Divide each side by '-1'. x = 9 Simplifying x = 9Solution
x = {-15, 9}
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