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Simplifying 64x3 = x Solving 64x3 = x Solving for variable 'x'. Reorder the terms: -1x + 64x3 = x + -1x Combine like terms: x + -1x = 0 -1x + 64x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-1 + 64x2) = 0 Factor a difference between two squares. x((1 + 8x)(-1 + 8x)) = 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 '(1 + 8x)' equal to zero and attempt to solve: Simplifying 1 + 8x = 0 Solving 1 + 8x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 8x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 8x = 0 + -1 8x = 0 + -1 Combine like terms: 0 + -1 = -1 8x = -1 Divide each side by '8'. x = -0.125 Simplifying x = -0.125Subproblem 3
Set the factor '(-1 + 8x)' equal to zero and attempt to solve: Simplifying -1 + 8x = 0 Solving -1 + 8x = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + 8x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 8x = 0 + 1 8x = 0 + 1 Combine like terms: 0 + 1 = 1 8x = 1 Divide each side by '8'. x = 0.125 Simplifying x = 0.125Solution
x = {0, -0.125, 0.125}
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