x^8=1

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Solution for x^8=1 equation: 


Simplifying
x8 = 1

Solving
x8 = 1

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Simplifying
x8 = 1

Reorder the terms:
-1 + x8 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + x8 = 0

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

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

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


Subproblem 1
Set the factor '(1 + x4)' equal to zero and attempt to solve:

Simplifying
1 + x4 = 0

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

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

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

Simplifying
x4 = -1

The solution to this equation could not be determined.

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

Subproblem 2
Set the factor '(1 + x2)' equal to zero and attempt to solve:

Simplifying
1 + x2 = 0

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

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

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

Simplifying
x2 = -1

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 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

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

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

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

Simplifying
x = -1

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

Simplifying
-1 + x = 0

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

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

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

Simplifying
x = 1
Solution
x = {-1, 1}

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