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Simplifying x(x2 + -8) = 8x Reorder the terms: x(-8 + x2) = 8x (-8 * x + x2 * x) = 8x (-8x + x3) = 8x Solving -8x + x3 = 8x Solving for variable 'x'. Reorder the terms: -8x + -8x + x3 = 8x + -8x Combine like terms: -8x + -8x = -16x -16x + x3 = 8x + -8x Combine like terms: 8x + -8x = 0 -16x + x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-16 + x2) = 0 Factor a difference between two squares. x((4 + x)(-4 + x)) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4Subproblem 3
Set the factor '(-4 + x)' equal to zero and attempt to solve: Simplifying -4 + x = 0 Solving -4 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + x = 0 + 4 x = 0 + 4 Combine like terms: 0 + 4 = 4 x = 4 Simplifying x = 4Solution
x = {0, -4, 4}
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