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Simplifying 2 = x2 + 8x + 17 Reorder the terms: 2 = 17 + 8x + x2 Solving 2 = 17 + 8x + x2 Solving for variable 'x'. Combine like terms: 2 + -17 = -15 -15 + -8x + -1x2 = 17 + 8x + x2 + -17 + -8x + -1x2 Reorder the terms: -15 + -8x + -1x2 = 17 + -17 + 8x + -8x + x2 + -1x2 Combine like terms: 17 + -17 = 0 -15 + -8x + -1x2 = 0 + 8x + -8x + x2 + -1x2 -15 + -8x + -1x2 = 8x + -8x + x2 + -1x2 Combine like terms: 8x + -8x = 0 -15 + -8x + -1x2 = 0 + x2 + -1x2 -15 + -8x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -15 + -8x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(15 + 8x + x2) = 0 Factor a trinomial. -1((5 + x)(3 + x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(5 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 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 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Simplifying x = -5Subproblem 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 = {-5, -3}
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