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Simplifying -3x + 6 = x2 + 8x + 16 Reorder the terms: 6 + -3x = x2 + 8x + 16 Reorder the terms: 6 + -3x = 16 + 8x + x2 Solving 6 + -3x = 16 + 8x + x2 Solving for variable 'x'. Reorder the terms: 6 + -16 + -3x + -8x + -1x2 = 16 + 8x + x2 + -16 + -8x + -1x2 Combine like terms: 6 + -16 = -10 -10 + -3x + -8x + -1x2 = 16 + 8x + x2 + -16 + -8x + -1x2 Combine like terms: -3x + -8x = -11x -10 + -11x + -1x2 = 16 + 8x + x2 + -16 + -8x + -1x2 Reorder the terms: -10 + -11x + -1x2 = 16 + -16 + 8x + -8x + x2 + -1x2 Combine like terms: 16 + -16 = 0 -10 + -11x + -1x2 = 0 + 8x + -8x + x2 + -1x2 -10 + -11x + -1x2 = 8x + -8x + x2 + -1x2 Combine like terms: 8x + -8x = 0 -10 + -11x + -1x2 = 0 + x2 + -1x2 -10 + -11x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -10 + -11x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(10 + 11x + x2) = 0 Factor a trinomial. -1((10 + x)(1 + x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(10 + x)' equal to zero and attempt to solve: Simplifying 10 + x = 0 Solving 10 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + x = 0 + -10 x = 0 + -10 Combine like terms: 0 + -10 = -10 x = -10 Simplifying x = -10Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1Solution
x = {-10, -1}
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