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Simplifying 0 = x4 + 14x2 + 24 Reorder the terms: 0 = 24 + 14x2 + x4 Solving 0 = 24 + 14x2 + x4 Solving for variable 'x'. Combine like terms: 0 + -24 = -24 -24 + -14x2 + -1x4 = 24 + 14x2 + x4 + -24 + -14x2 + -1x4 Reorder the terms: -24 + -14x2 + -1x4 = 24 + -24 + 14x2 + -14x2 + x4 + -1x4 Combine like terms: 24 + -24 = 0 -24 + -14x2 + -1x4 = 0 + 14x2 + -14x2 + x4 + -1x4 -24 + -14x2 + -1x4 = 14x2 + -14x2 + x4 + -1x4 Combine like terms: 14x2 + -14x2 = 0 -24 + -14x2 + -1x4 = 0 + x4 + -1x4 -24 + -14x2 + -1x4 = x4 + -1x4 Combine like terms: x4 + -1x4 = 0 -24 + -14x2 + -1x4 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(24 + 14x2 + x4) = 0 Factor a trinomial. -1((12 + x2)(2 + x2)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(12 + x2)' equal to zero and attempt to solve: Simplifying 12 + x2 = 0 Solving 12 + x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + x2 = 0 + -12 x2 = 0 + -12 Combine like terms: 0 + -12 = -12 x2 = -12 Simplifying x2 = -12 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 '(2 + x2)' equal to zero and attempt to solve: Simplifying 2 + x2 = 0 Solving 2 + x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x2 = 0 + -2 x2 = 0 + -2 Combine like terms: 0 + -2 = -2 x2 = -2 Simplifying x2 = -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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