x^100-1=0

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Solution for x^100-1=0 equation:


Simplifying
x100 + -1 = 0

Reorder the terms:
-1 + x100 = 0

Solving
-1 + x100 = 0

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x100 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + x100 = 0 + 1
x100 = 0 + 1

Combine like terms: 0 + 1 = 1
x100 = 1

Simplifying
x100 = 1

Reorder the terms:
-1 + x100 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + x100 = 0

Factor a difference between two squares.
(1 + x50)(-1 + x50) = 0

Factor a difference between two squares.
(1 + x50)((1 + x25)(-1 + x25)) = 0

Subproblem 1

Set the factor '(1 + x50)' equal to zero and attempt to solve: Simplifying 1 + x50 = 0 Solving 1 + x50 = 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 + x50 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x50 = 0 + -1 x50 = 0 + -1 Combine like terms: 0 + -1 = -1 x50 = -1 Simplifying x50 = -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 + x25)' equal to zero and attempt to solve: Simplifying 1 + x25 = 0 Solving 1 + x25 = 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 + x25 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x25 = 0 + -1 x25 = 0 + -1 Combine like terms: 0 + -1 = -1 x25 = -1 Simplifying x25 = -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 + x25)' equal to zero and attempt to solve: Simplifying -1 + x25 = 0 Solving -1 + x25 = 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 + x25 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + x25 = 0 + 1 x25 = 0 + 1 Combine like terms: 0 + 1 = 1 x25 = 1 Simplifying x25 = 1 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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