a^8-1=0

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Solution for a^8-1=0 equation:


Simplifying
a8 + -1 = 0

Reorder the terms:
-1 + a8 = 0

Solving
-1 + a8 = 0

Solving for variable 'a'.

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

Add '1' to each side of the equation.
-1 + 1 + a8 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + a8 = 0 + 1
a8 = 0 + 1

Combine like terms: 0 + 1 = 1
a8 = 1

Simplifying
a8 = 1

Reorder the terms:
-1 + a8 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + a8 = 0

Factor a difference between two squares.
(1 + a4)(-1 + a4) = 0

Factor a difference between two squares.
(1 + a4)((1 + a2)(-1 + a2)) = 0

Factor a difference between two squares.
(1 + a4)((1 + a2)((1 + a)(-1 + a))) = 0

Subproblem 1

Set the factor '(1 + a4)' equal to zero and attempt to solve: Simplifying 1 + a4 = 0 Solving 1 + a4 = 0 Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + a4 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + a4 = 0 + -1 a4 = 0 + -1 Combine like terms: 0 + -1 = -1 a4 = -1 Simplifying a4 = -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 + a2)' equal to zero and attempt to solve: Simplifying 1 + a2 = 0 Solving 1 + a2 = 0 Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + a2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + a2 = 0 + -1 a2 = 0 + -1 Combine like terms: 0 + -1 = -1 a2 = -1 Simplifying a2 = -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 + a)' equal to zero and attempt to solve: Simplifying 1 + a = 0 Solving 1 + a = 0 Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + a = 0 + -1 a = 0 + -1 Combine like terms: 0 + -1 = -1 a = -1 Simplifying a = -1

Subproblem 4

Set the factor '(-1 + a)' equal to zero and attempt to solve: Simplifying -1 + a = 0 Solving -1 + a = 0 Move all terms containing a to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + a = 0 + 1 Combine like terms: -1 + 1 = 0 0 + a = 0 + 1 a = 0 + 1 Combine like terms: 0 + 1 = 1 a = 1 Simplifying a = 1

Solution

a = {-1, 1}

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