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Simplifying 5 + -3x + -2x2 = x2 + -13 Reorder the terms: 5 + -3x + -2x2 = -13 + x2 Solving 5 + -3x + -2x2 = -13 + x2 Solving for variable 'x'. Reorder the terms: 5 + 13 + -3x + -2x2 + -1x2 = -13 + x2 + 13 + -1x2 Combine like terms: 5 + 13 = 18 18 + -3x + -2x2 + -1x2 = -13 + x2 + 13 + -1x2 Combine like terms: -2x2 + -1x2 = -3x2 18 + -3x + -3x2 = -13 + x2 + 13 + -1x2 Reorder the terms: 18 + -3x + -3x2 = -13 + 13 + x2 + -1x2 Combine like terms: -13 + 13 = 0 18 + -3x + -3x2 = 0 + x2 + -1x2 18 + -3x + -3x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 18 + -3x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(6 + -1x + -1x2) = 0 Factor a trinomial. 3((2 + -1x)(3 + x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Subproblem 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 = {2, -3}
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