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Simplifying 4x^{4}+ 3x^{2}+ -1 = 0 Reorder the terms: -1 + 3x^{2}+ 4x^{4}= 0 Solving -1 + 3x^{2}+ 4x^{4}= 0 Solving for variable 'x'. Factor a trinomial. (-1 + -1x^{2})(1 + -4x^{2}) = 0 Factor a difference between two squares. (-1 + -1x^{2})((1 + 2x)(1 + -2x)) = 0## Subproblem 1

Set the factor '(-1 + -1x^{2})' equal to zero and attempt to solve: Simplifying -1 + -1x^{2}= 0 Solving -1 + -1x^{2}= 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 + -1x^{2}= 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1x^{2}= 0 + 1 -1x^{2}= 0 + 1 Combine like terms: 0 + 1 = 1 -1x^{2}= 1 Divide each side by '-1'. x^{2}= -1 Simplifying x^{2}= -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 + 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 = -0.5## Subproblem 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 = 0.5## Solution

x = {-0.5, 0.5}

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