z^8-1=8

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Solution for z^8-1=8 equation:


Simplifying
z8 + -1 = 8

Reorder the terms:
-1 + z8 = 8

Solving
-1 + z8 = 8

Solving for variable 'z'.

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

Add '1' to each side of the equation.
-1 + 1 + z8 = 8 + 1

Combine like terms: -1 + 1 = 0
0 + z8 = 8 + 1
z8 = 8 + 1

Combine like terms: 8 + 1 = 9
z8 = 9

Simplifying
z8 = 9

Reorder the terms:
-9 + z8 = 9 + -9

Combine like terms: 9 + -9 = 0
-9 + z8 = 0

Factor a difference between two squares.
(3 + z4)(-3 + z4) = 0

Subproblem 1

Set the factor '(3 + z4)' equal to zero and attempt to solve: Simplifying 3 + z4 = 0 Solving 3 + z4 = 0 Move all terms containing z to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + z4 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + z4 = 0 + -3 z4 = 0 + -3 Combine like terms: 0 + -3 = -3 z4 = -3 Simplifying z4 = -3 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 '(-3 + z4)' equal to zero and attempt to solve: Simplifying -3 + z4 = 0 Solving -3 + z4 = 0 Move all terms containing z to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + z4 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + z4 = 0 + 3 z4 = 0 + 3 Combine like terms: 0 + 3 = 3 z4 = 3 Simplifying z4 = 3 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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