s^8-1=0

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Solution for s^8-1=0 equation: 


Simplifying
s8 + -1 = 0

Reorder the terms:
-1 + s8 = 0

Solving
-1 + s8 = 0

Solving for variable 's'.

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

Add '1' to each side of the equation.
-1 + 1 + s8 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + s8 = 0 + 1
s8 = 0 + 1

Combine like terms: 0 + 1 = 1
s8 = 1

Simplifying
s8 = 1

Reorder the terms:
-1 + s8 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + s8 = 0

Factor a difference between two squares.
(1 + s4)(-1 + s4) = 0

Factor a difference between two squares.
(1 + s4)((1 + s2)(-1 + s2)) = 0

Factor a difference between two squares.
(1 + s4)((1 + s2)((1 + s)(-1 + s))) = 0


Subproblem 1
Set the factor '(1 + s4)' equal to zero and attempt to solve:

Simplifying
1 + s4 = 0

Solving
1 + s4 = 0

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

Add '-1' to each side of the equation.
1 + -1 + s4 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + s4 = 0 + -1
s4 = 0 + -1

Combine like terms: 0 + -1 = -1
s4 = -1

Simplifying
s4 = -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 + s2)' equal to zero and attempt to solve:

Simplifying
1 + s2 = 0

Solving
1 + s2 = 0

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

Add '-1' to each side of the equation.
1 + -1 + s2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + s2 = 0 + -1
s2 = 0 + -1

Combine like terms: 0 + -1 = -1
s2 = -1

Simplifying
s2 = -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 + s)' equal to zero and attempt to solve:

Simplifying
1 + s = 0

Solving
1 + s = 0

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

Add '-1' to each side of the equation.
1 + -1 + s = 0 + -1

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

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

Simplifying
s = -1

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

Simplifying
-1 + s = 0

Solving
-1 + s = 0

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

Add '1' to each side of the equation.
-1 + 1 + s = 0 + 1

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

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

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

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