0=x^5-64x

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Solution for 0=x^5-64x equation: 


Simplifying
0 = x5 + -64x

Reorder the terms:
0 = -64x + x5

Solving
0 = -64x + x5

Solving for variable 'x'.
Remove the zero:
64x + -1x5 = -64x + x5 + 64x + -1x5

Reorder the terms:
64x + -1x5 = -64x + 64x + x5 + -1x5

Combine like terms: -64x + 64x = 0
64x + -1x5 = 0 + x5 + -1x5
64x + -1x5 = x5 + -1x5

Combine like terms: x5 + -1x5 = 0
64x + -1x5 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(64 + -1x4) = 0

Factor a difference between two squares.
x((8 + x2)(8 + -1x2)) = 0


Subproblem 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 = 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 + -1x2)' equal to zero and attempt to solve:

Simplifying
8 + -1x2 = 0

Solving
8 + -1x2 = 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 + -1x2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x2 = 0 + -8
-1x2 = 0 + -8

Combine like terms: 0 + -8 = -8
-1x2 = -8

Divide each side by '-1'.
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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