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Simplifying 10q8 + -10 = 0 Reorder the terms: -10 + 10q8 = 0 Solving -10 + 10q8 = 0 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + 10q8 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 10q8 = 0 + 10 10q8 = 0 + 10 Combine like terms: 0 + 10 = 10 10q8 = 10 Divide each side by '10'. q8 = 1 Simplifying q8 = 1 Reorder the terms: -1 + q8 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + q8 = 0 Factor a difference between two squares. (1 + q4)(-1 + q4) = 0 Factor a difference between two squares. (1 + q4)((1 + q2)(-1 + q2)) = 0 Factor a difference between two squares. (1 + q4)((1 + q2)((1 + q)(-1 + q))) = 0Subproblem 1
Set the factor '(1 + q4)' equal to zero and attempt to solve: Simplifying 1 + q4 = 0 Solving 1 + q4 = 0 Move all terms containing q to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + q4 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + q4 = 0 + -1 q4 = 0 + -1 Combine like terms: 0 + -1 = -1 q4 = -1 Simplifying q4 = -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 + q2)' equal to zero and attempt to solve: Simplifying 1 + q2 = 0 Solving 1 + q2 = 0 Move all terms containing q to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + q2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + q2 = 0 + -1 q2 = 0 + -1 Combine like terms: 0 + -1 = -1 q2 = -1 Simplifying q2 = -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 + q)' equal to zero and attempt to solve: Simplifying 1 + q = 0 Solving 1 + q = 0 Move all terms containing q to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + q = 0 + -1 Combine like terms: 1 + -1 = 0 0 + q = 0 + -1 q = 0 + -1 Combine like terms: 0 + -1 = -1 q = -1 Simplifying q = -1Subproblem 4
Set the factor '(-1 + q)' equal to zero and attempt to solve: Simplifying -1 + q = 0 Solving -1 + q = 0 Move all terms containing q to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + q = 0 + 1 Combine like terms: -1 + 1 = 0 0 + q = 0 + 1 q = 0 + 1 Combine like terms: 0 + 1 = 1 q = 1 Simplifying q = 1Solution
q = {-1, 1}
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