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Simplifying 16x4 + 4x2 + -2 = 0 Reorder the terms: -2 + 4x2 + 16x4 = 0 Solving -2 + 4x2 + 16x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + 2x2 + 8x4) = 0 Factor a trinomial. 2((-1 + -2x2)(1 + -4x2)) = 0 Factor a difference between two squares. 2((-1 + -2x2)((1 + 2x)(1 + -2x))) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + -2x2)' equal to zero and attempt to solve: Simplifying -1 + -2x2 = 0 Solving -1 + -2x2 = 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 + -2x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2x2 = 0 + 1 -2x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -2x2 = 1 Divide each side by '-2'. x2 = -0.5 Simplifying x2 = -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 + 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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