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Simplifying x6 + -64x2 = 0 Reorder the terms: -64x2 + x6 = 0 Solving -64x2 + x6 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(-64 + x4) = 0 Factor a difference between two squares. x2((8 + x2)(-8 + x2)) = 0Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
Set the factor '(8 + x2)' equal to zero and attempt to solve: Simplifying 8 + x2 = 0 Solving 8 + x2 = 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 + x2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + x2 = 0 + -8 x2 = 0 + -8 Combine like terms: 0 + -8 = -8 x2 = -8 Simplifying x2 = -8 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(-8 + x2)' equal to zero and attempt to solve: Simplifying -8 + x2 = 0 Solving -8 + x2 = 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 + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + x2 = 0 + 8 x2 = 0 + 8 Combine like terms: 0 + 8 = 8 x2 = 8 Simplifying x2 = 8 Take the square root of each side: x = {-2.828427125, 2.828427125}Solution
x = {0, -2.828427125, 2.828427125}
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