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Simplifying x(2x + -12) = 182 Reorder the terms: x(-12 + 2x) = 182 (-12 * x + 2x * x) = 182 (-12x + 2x2) = 182 Solving -12x + 2x2 = 182 Solving for variable 'x'. Reorder the terms: -182 + -12x + 2x2 = 182 + -182 Combine like terms: 182 + -182 = 0 -182 + -12x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-91 + -6x + x2) = 0 Factor a trinomial. 2((-7 + -1x)(13 + -1x)) = 0 Ignore the factor 2.Subproblem 1
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 = -7Subproblem 2
Set the factor '(13 + -1x)' equal to zero and attempt to solve: Simplifying 13 + -1x = 0 Solving 13 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + -1x = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -1x = 0 + -13 -1x = 0 + -13 Combine like terms: 0 + -13 = -13 -1x = -13 Divide each side by '-1'. x = 13 Simplifying x = 13Solution
x = {-7, 13}
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