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Simplifying 5x^{4}+ 31x^{2}+ 6 = 0 Reorder the terms: 6 + 31x^{2}+ 5x^{4}= 0 Solving 6 + 31x^{2}+ 5x^{4}= 0 Solving for variable 'x'. Factor a trinomial. (6 + x^{2})(1 + 5x^{2}) = 0## Subproblem 1

Set the factor '(6 + x^{2})' equal to zero and attempt to solve: Simplifying 6 + x^{2}= 0 Solving 6 + x^{2}= 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x^{2}= 0 + -6 Combine like terms: 6 + -6 = 0 0 + x^{2}= 0 + -6 x^{2}= 0 + -6 Combine like terms: 0 + -6 = -6 x^{2}= -6 Simplifying x^{2}= -6 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 + 5x^{2})' equal to zero and attempt to solve: Simplifying 1 + 5x^{2}= 0 Solving 1 + 5x^{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 + 5x^{2}= 0 + -1 Combine like terms: 1 + -1 = 0 0 + 5x^{2}= 0 + -1 5x^{2}= 0 + -1 Combine like terms: 0 + -1 = -1 5x^{2}= -1 Divide each side by '5'. x^{2}= -0.2 Simplifying x^{2}= -0.2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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