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Simplifying 0 = 16x4 + 8x2 + -3 Reorder the terms: 0 = -3 + 8x2 + 16x4 Solving 0 = -3 + 8x2 + 16x4 Solving for variable 'x'. Combine like terms: 0 + 3 = 3 3 + -8x2 + -16x4 = -3 + 8x2 + 16x4 + 3 + -8x2 + -16x4 Reorder the terms: 3 + -8x2 + -16x4 = -3 + 3 + 8x2 + -8x2 + 16x4 + -16x4 Combine like terms: -3 + 3 = 0 3 + -8x2 + -16x4 = 0 + 8x2 + -8x2 + 16x4 + -16x4 3 + -8x2 + -16x4 = 8x2 + -8x2 + 16x4 + -16x4 Combine like terms: 8x2 + -8x2 = 0 3 + -8x2 + -16x4 = 0 + 16x4 + -16x4 3 + -8x2 + -16x4 = 16x4 + -16x4 Combine like terms: 16x4 + -16x4 = 0 3 + -8x2 + -16x4 = 0 Factor a trinomial. (1 + -4x2)(3 + 4x2) = 0 Factor a difference between two squares. ((1 + 2x)(1 + -2x))(3 + 4x2) = 0Subproblem 1
Set the factor '(3 + 4x2)' equal to zero and attempt to solve: Simplifying 3 + 4x2 = 0 Solving 3 + 4x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 4x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4x2 = 0 + -3 4x2 = 0 + -3 Combine like terms: 0 + -3 = -3 4x2 = -3 Divide each side by '4'. x2 = -0.75 Simplifying x2 = -0.75 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 + 2x)' equal to zero and attempt to solve: Simplifying 1 + 2x = 0 Solving 1 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2x = 0 + -1 2x = 0 + -1 Combine like terms: 0 + -1 = -1 2x = -1 Divide each side by '2'. x = -0.5 Simplifying x = -0.5Subproblem 3
Set the factor '(1 + -2x)' equal to zero and attempt to solve: Simplifying 1 + -2x = 0 Solving 1 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x = 0 + -1 -2x = 0 + -1 Combine like terms: 0 + -1 = -1 -2x = -1 Divide each side by '-2'. x = 0.5 Simplifying x = 0.5Solution
x = {-0.5, 0.5}
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