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Simplifying 5 = x2 + 8x + 17 Reorder the terms: 5 = 17 + 8x + x2 Solving 5 = 17 + 8x + x2 Solving for variable 'x'. Combine like terms: 5 + -17 = -12 -12 + -8x + -1x2 = 17 + 8x + x2 + -17 + -8x + -1x2 Reorder the terms: -12 + -8x + -1x2 = 17 + -17 + 8x + -8x + x2 + -1x2 Combine like terms: 17 + -17 = 0 -12 + -8x + -1x2 = 0 + 8x + -8x + x2 + -1x2 -12 + -8x + -1x2 = 8x + -8x + x2 + -1x2 Combine like terms: 8x + -8x = 0 -12 + -8x + -1x2 = 0 + x2 + -1x2 -12 + -8x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -12 + -8x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(12 + 8x + x2) = 0 Factor a trinomial. -1((6 + x)(2 + x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(6 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 x = -6 Simplifying x = -6Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 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 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Solution
x = {-6, -2}
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