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Simplifying x3 + 18x2 = 2x2 + -64x Reorder the terms: 18x2 + x3 = 2x2 + -64x Reorder the terms: 18x2 + x3 = -64x + 2x2 Solving 18x2 + x3 = -64x + 2x2 Solving for variable 'x'. Reorder the terms: 64x + 18x2 + -2x2 + x3 = -64x + 2x2 + 64x + -2x2 Combine like terms: 18x2 + -2x2 = 16x2 64x + 16x2 + x3 = -64x + 2x2 + 64x + -2x2 Reorder the terms: 64x + 16x2 + x3 = -64x + 64x + 2x2 + -2x2 Combine like terms: -64x + 64x = 0 64x + 16x2 + x3 = 0 + 2x2 + -2x2 64x + 16x2 + x3 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 64x + 16x2 + x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(64 + 16x + x2) = 0 Factor a trinomial. x((8 + x)(8 + 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 '(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 = -8Subproblem 3
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 = {0, -8, -8}
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