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Simplifying 16u8 + -8u4 + 1 = 0 Reorder the terms: 1 + -8u4 + 16u8 = 0 Solving 1 + -8u4 + 16u8 = 0 Solving for variable 'u'. Factor a trinomial. (1 + -4u4)(1 + -4u4) = 0 Factor a difference between two squares. ((1 + 2u2)(1 + -2u2))(1 + -4u4) = 0 Factor a difference between two squares. ((1 + 2u2)(1 + -2u2))(1 + 2u2)(1 + -2u2) = 0Subproblem 1
Set the factor '(1 + 2u2)' equal to zero and attempt to solve: Simplifying 1 + 2u2 = 0 Solving 1 + 2u2 = 0 Move all terms containing u to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2u2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2u2 = 0 + -1 2u2 = 0 + -1 Combine like terms: 0 + -1 = -1 2u2 = -1 Divide each side by '2'. u2 = -0.5 Simplifying u2 = -0.5 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 + -2u2)' equal to zero and attempt to solve: Simplifying 1 + -2u2 = 0 Solving 1 + -2u2 = 0 Move all terms containing u to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2u2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2u2 = 0 + -1 -2u2 = 0 + -1 Combine like terms: 0 + -1 = -1 -2u2 = -1 Divide each side by '-2'. u2 = 0.5 Simplifying u2 = 0.5 Take the square root of each side: u = {-0.707106781, 0.707106781}Subproblem 3
Set the factor '(1 + 2u2)' equal to zero and attempt to solve: Simplifying 1 + 2u2 = 0 Solving 1 + 2u2 = 0 Move all terms containing u to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2u2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2u2 = 0 + -1 2u2 = 0 + -1 Combine like terms: 0 + -1 = -1 2u2 = -1 Divide each side by '2'. u2 = -0.5 Simplifying u2 = -0.5 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 4
Set the factor '(1 + -2u2)' equal to zero and attempt to solve: Simplifying 1 + -2u2 = 0 Solving 1 + -2u2 = 0 Move all terms containing u to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2u2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2u2 = 0 + -1 -2u2 = 0 + -1 Combine like terms: 0 + -1 = -1 -2u2 = -1 Divide each side by '-2'. u2 = 0.5 Simplifying u2 = 0.5 Take the square root of each side: u = {-0.707106781, 0.707106781}Solution
u = {-0.707106781, 0.707106781, -0.707106781, 0.707106781}
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