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Simplifying 8 + -7x = x2 + 32x + 256 Reorder the terms: 8 + -7x = 256 + 32x + x2 Solving 8 + -7x = 256 + 32x + x2 Solving for variable 'x'. Reorder the terms: 8 + -256 + -7x + -32x + -1x2 = 256 + 32x + x2 + -256 + -32x + -1x2 Combine like terms: 8 + -256 = -248 -248 + -7x + -32x + -1x2 = 256 + 32x + x2 + -256 + -32x + -1x2 Combine like terms: -7x + -32x = -39x -248 + -39x + -1x2 = 256 + 32x + x2 + -256 + -32x + -1x2 Reorder the terms: -248 + -39x + -1x2 = 256 + -256 + 32x + -32x + x2 + -1x2 Combine like terms: 256 + -256 = 0 -248 + -39x + -1x2 = 0 + 32x + -32x + x2 + -1x2 -248 + -39x + -1x2 = 32x + -32x + x2 + -1x2 Combine like terms: 32x + -32x = 0 -248 + -39x + -1x2 = 0 + x2 + -1x2 -248 + -39x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -248 + -39x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(248 + 39x + x2) = 0 Factor a trinomial. -1((31 + x)(8 + x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(31 + x)' equal to zero and attempt to solve: Simplifying 31 + x = 0 Solving 31 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-31' to each side of the equation. 31 + -31 + x = 0 + -31 Combine like terms: 31 + -31 = 0 0 + x = 0 + -31 x = 0 + -31 Combine like terms: 0 + -31 = -31 x = -31 Simplifying x = -31Subproblem 2
Set the factor '(8 + x)' equal to zero and attempt to solve: Simplifying 8 + x = 0 Solving 8 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + x = 0 + -8 x = 0 + -8 Combine like terms: 0 + -8 = -8 x = -8 Simplifying x = -8Solution
x = {-31, -8}
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