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Simplifying x2 + x + -2 = 16 + -1x2 + -3x + 12 Reorder the terms: -2 + x + x2 = 16 + -1x2 + -3x + 12 Reorder the terms: -2 + x + x2 = 16 + 12 + -3x + -1x2 Combine like terms: 16 + 12 = 28 -2 + x + x2 = 28 + -3x + -1x2 Solving -2 + x + x2 = 28 + -3x + -1x2 Solving for variable 'x'. Reorder the terms: -2 + -28 + x + 3x + x2 + x2 = 28 + -3x + -1x2 + -28 + 3x + x2 Combine like terms: -2 + -28 = -30 -30 + x + 3x + x2 + x2 = 28 + -3x + -1x2 + -28 + 3x + x2 Combine like terms: x + 3x = 4x -30 + 4x + x2 + x2 = 28 + -3x + -1x2 + -28 + 3x + x2 Combine like terms: x2 + x2 = 2x2 -30 + 4x + 2x2 = 28 + -3x + -1x2 + -28 + 3x + x2 Reorder the terms: -30 + 4x + 2x2 = 28 + -28 + -3x + 3x + -1x2 + x2 Combine like terms: 28 + -28 = 0 -30 + 4x + 2x2 = 0 + -3x + 3x + -1x2 + x2 -30 + 4x + 2x2 = -3x + 3x + -1x2 + x2 Combine like terms: -3x + 3x = 0 -30 + 4x + 2x2 = 0 + -1x2 + x2 -30 + 4x + 2x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -30 + 4x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-15 + 2x + x2) = 0 Factor a trinomial. 2((-5 + -1x)(3 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve: Simplifying -5 + -1x = 0 Solving -5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1x = 0 + 5 -1x = 0 + 5 Combine like terms: 0 + 5 = 5 -1x = 5 Divide each side by '-1'. x = -5 Simplifying x = -5Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solution
x = {-5, 3}
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