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Simplifying -2x2 + -18x + -34 = -1x2 + -11x + -22 Reorder the terms: -34 + -18x + -2x2 = -1x2 + -11x + -22 Reorder the terms: -34 + -18x + -2x2 = -22 + -11x + -1x2 Solving -34 + -18x + -2x2 = -22 + -11x + -1x2 Solving for variable 'x'. Reorder the terms: -34 + 22 + -18x + 11x + -2x2 + x2 = -22 + -11x + -1x2 + 22 + 11x + x2 Combine like terms: -34 + 22 = -12 -12 + -18x + 11x + -2x2 + x2 = -22 + -11x + -1x2 + 22 + 11x + x2 Combine like terms: -18x + 11x = -7x -12 + -7x + -2x2 + x2 = -22 + -11x + -1x2 + 22 + 11x + x2 Combine like terms: -2x2 + x2 = -1x2 -12 + -7x + -1x2 = -22 + -11x + -1x2 + 22 + 11x + x2 Reorder the terms: -12 + -7x + -1x2 = -22 + 22 + -11x + 11x + -1x2 + x2 Combine like terms: -22 + 22 = 0 -12 + -7x + -1x2 = 0 + -11x + 11x + -1x2 + x2 -12 + -7x + -1x2 = -11x + 11x + -1x2 + x2 Combine like terms: -11x + 11x = 0 -12 + -7x + -1x2 = 0 + -1x2 + x2 -12 + -7x + -1x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -12 + -7x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(12 + 7x + x2) = 0 Factor a trinomial. -1((4 + x)(3 + x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 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 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3Solution
x = {-4, -3}
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