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Simplifying Z8 = 1 Solving Z8 = 1 Solving for variable 'Z'. Move all terms containing Z to the left, all other terms to the right. Simplifying Z8 = 1 Reorder the terms: -1 + Z8 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + Z8 = 0 Factor a difference between two squares. (1 + Z4)(-1 + Z4) = 0 Factor a difference between two squares. (1 + Z4)((1 + Z2)(-1 + Z2)) = 0 Factor a difference between two squares. (1 + Z4)((1 + Z2)((1 + Z)(-1 + Z))) = 0Subproblem 1
Set the factor '(1 + Z4)' equal to zero and attempt to solve: Simplifying 1 + Z4 = 0 Solving 1 + Z4 = 0 Move all terms containing Z to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + Z4 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + Z4 = 0 + -1 Z4 = 0 + -1 Combine like terms: 0 + -1 = -1 Z4 = -1 Simplifying Z4 = -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 + Z2)' equal to zero and attempt to solve: Simplifying 1 + Z2 = 0 Solving 1 + Z2 = 0 Move all terms containing Z to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + Z2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + Z2 = 0 + -1 Z2 = 0 + -1 Combine like terms: 0 + -1 = -1 Z2 = -1 Simplifying Z2 = -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 + Z)' equal to zero and attempt to solve: Simplifying 1 + Z = 0 Solving 1 + Z = 0 Move all terms containing Z to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + Z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + Z = 0 + -1 Z = 0 + -1 Combine like terms: 0 + -1 = -1 Z = -1 Simplifying Z = -1Subproblem 4
Set the factor '(-1 + Z)' equal to zero and attempt to solve: Simplifying -1 + Z = 0 Solving -1 + Z = 0 Move all terms containing Z to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + Z = 0 + 1 Combine like terms: -1 + 1 = 0 0 + Z = 0 + 1 Z = 0 + 1 Combine like terms: 0 + 1 = 1 Z = 1 Simplifying Z = 1Solution
Z = {-1, 1}
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