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Simplifying 2x2 + 16x + 64 = x2 + 32x + 256 Reorder the terms: 64 + 16x + 2x2 = x2 + 32x + 256 Reorder the terms: 64 + 16x + 2x2 = 256 + 32x + x2 Solving 64 + 16x + 2x2 = 256 + 32x + x2 Solving for variable 'x'. Reorder the terms: 64 + -256 + 16x + -32x + 2x2 + -1x2 = 256 + 32x + x2 + -256 + -32x + -1x2 Combine like terms: 64 + -256 = -192 -192 + 16x + -32x + 2x2 + -1x2 = 256 + 32x + x2 + -256 + -32x + -1x2 Combine like terms: 16x + -32x = -16x -192 + -16x + 2x2 + -1x2 = 256 + 32x + x2 + -256 + -32x + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 -192 + -16x + 1x2 = 256 + 32x + x2 + -256 + -32x + -1x2 Reorder the terms: -192 + -16x + 1x2 = 256 + -256 + 32x + -32x + x2 + -1x2 Combine like terms: 256 + -256 = 0 -192 + -16x + 1x2 = 0 + 32x + -32x + x2 + -1x2 -192 + -16x + 1x2 = 32x + -32x + x2 + -1x2 Combine like terms: 32x + -32x = 0 -192 + -16x + 1x2 = 0 + x2 + -1x2 -192 + -16x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -192 + -16x + 1x2 = 0 Factor a trinomial. (-8 + -1x)(24 + -1x) = 0Subproblem 1
Set the factor '(-8 + -1x)' equal to zero and attempt to solve: Simplifying -8 + -1x = 0 Solving -8 + -1x = 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 + -1x = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1x = 0 + 8 -1x = 0 + 8 Combine like terms: 0 + 8 = 8 -1x = 8 Divide each side by '-1'. x = -8 Simplifying x = -8Subproblem 2
Set the factor '(24 + -1x)' equal to zero and attempt to solve: Simplifying 24 + -1x = 0 Solving 24 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-24' to each side of the equation. 24 + -24 + -1x = 0 + -24 Combine like terms: 24 + -24 = 0 0 + -1x = 0 + -24 -1x = 0 + -24 Combine like terms: 0 + -24 = -24 -1x = -24 Divide each side by '-1'. x = 24 Simplifying x = 24Solution
x = {-8, 24}
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