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Simplifying 16q4 + -8q2 + 1 = 0 Reorder the terms: 1 + -8q2 + 16q4 = 0 Solving 1 + -8q2 + 16q4 = 0 Solving for variable 'q'. Factor a trinomial. (1 + -4q2)(1 + -4q2) = 0 Factor a difference between two squares. ((1 + 2q)(1 + -2q))(1 + -4q2) = 0 Factor a difference between two squares. ((1 + 2q)(1 + -2q))(1 + 2q)(1 + -2q) = 0Subproblem 1
Set the factor '(1 + 2q)' equal to zero and attempt to solve: Simplifying 1 + 2q = 0 Solving 1 + 2q = 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 + 2q = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2q = 0 + -1 2q = 0 + -1 Combine like terms: 0 + -1 = -1 2q = -1 Divide each side by '2'. q = -0.5 Simplifying q = -0.5Subproblem 2
Set the factor '(1 + -2q)' equal to zero and attempt to solve: Simplifying 1 + -2q = 0 Solving 1 + -2q = 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 + -2q = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2q = 0 + -1 -2q = 0 + -1 Combine like terms: 0 + -1 = -1 -2q = -1 Divide each side by '-2'. q = 0.5 Simplifying q = 0.5Subproblem 3
Set the factor '(1 + 2q)' equal to zero and attempt to solve: Simplifying 1 + 2q = 0 Solving 1 + 2q = 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 + 2q = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2q = 0 + -1 2q = 0 + -1 Combine like terms: 0 + -1 = -1 2q = -1 Divide each side by '2'. q = -0.5 Simplifying q = -0.5Subproblem 4
Set the factor '(1 + -2q)' equal to zero and attempt to solve: Simplifying 1 + -2q = 0 Solving 1 + -2q = 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 + -2q = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2q = 0 + -1 -2q = 0 + -1 Combine like terms: 0 + -1 = -1 -2q = -1 Divide each side by '-2'. q = 0.5 Simplifying q = 0.5Solution
q = {-0.5, 0.5, -0.5, 0.5}
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