256(x^9)-x=0

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Solution for 256(x^9)-x=0 equation: 


Simplifying
256(x9) + -1x = 0

Reorder the terms:
-1x + 256x9 = 0

Solving
-1x + 256x9 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-1 + 256x8) = 0

Factor a difference between two squares.
x((1 + 16x4)(-1 + 16x4)) = 0

Factor a difference between two squares.
x((1 + 16x4)((1 + 4x2)(-1 + 4x2))) = 0

Factor a difference between two squares.
x((1 + 16x4)((1 + 4x2)((1 + 2x)(-1 + 2x)))) = 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 '(1 + 16x4)' equal to zero and attempt to solve:

Simplifying
1 + 16x4 = 0

Solving
1 + 16x4 = 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 + 16x4 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 16x4 = 0 + -1
16x4 = 0 + -1

Combine like terms: 0 + -1 = -1
16x4 = -1

Divide each side by '16'.
x4 = -0.0625

Simplifying
x4 = -0.0625

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 '(1 + 4x2)' equal to zero and attempt to solve:

Simplifying
1 + 4x2 = 0

Solving
1 + 4x2 = 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 + 4x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4x2 = 0 + -1
4x2 = 0 + -1

Combine like terms: 0 + -1 = -1
4x2 = -1

Divide each side by '4'.
x2 = -0.25

Simplifying
x2 = -0.25

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 4
Set the factor '(1 + 2x)' equal to zero and attempt to solve:

Simplifying
1 + 2x = 0

Solving
1 + 2x = 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 + 2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2x = 0 + -1
2x = 0 + -1

Combine like terms: 0 + -1 = -1
2x = -1

Divide each side by '2'.
x = -0.5

Simplifying
x = -0.5

Subproblem 5
Set the factor '(-1 + 2x)' equal to zero and attempt to solve:

Simplifying
-1 + 2x = 0

Solving
-1 + 2x = 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 + 2x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 2x = 0 + 1
2x = 0 + 1

Combine like terms: 0 + 1 = 1
2x = 1

Divide each side by '2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {0, -0.5, 0.5}

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