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Simplifying 0 = 5x4 + 15x2 + 10 Reorder the terms: 0 = 10 + 15x2 + 5x4 Solving 0 = 10 + 15x2 + 5x4 Solving for variable 'x'. Combine like terms: 0 + -10 = -10 -10 + -15x2 + -5x4 = 10 + 15x2 + 5x4 + -10 + -15x2 + -5x4 Reorder the terms: -10 + -15x2 + -5x4 = 10 + -10 + 15x2 + -15x2 + 5x4 + -5x4 Combine like terms: 10 + -10 = 0 -10 + -15x2 + -5x4 = 0 + 15x2 + -15x2 + 5x4 + -5x4 -10 + -15x2 + -5x4 = 15x2 + -15x2 + 5x4 + -5x4 Combine like terms: 15x2 + -15x2 = 0 -10 + -15x2 + -5x4 = 0 + 5x4 + -5x4 -10 + -15x2 + -5x4 = 5x4 + -5x4 Combine like terms: 5x4 + -5x4 = 0 -10 + -15x2 + -5x4 = 0 Factor out the Greatest Common Factor (GCF), '-5'. -5(2 + 3x2 + x4) = 0 Factor a trinomial. -5((2 + x2)(1 + x2)) = 0 Ignore the factor -5.Subproblem 1
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.Subproblem 2
Set the factor '(1 + x2)' equal to zero and attempt to solve: Simplifying 1 + x2 = 0 Solving 1 + x2 = 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 + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x2 = 0 + -1 x2 = 0 + -1 Combine like terms: 0 + -1 = -1 x2 = -1 Simplifying x2 = -1 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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