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Simplifying 2x4 + -4x2 + -1 = 15 Reorder the terms: -1 + -4x2 + 2x4 = 15 Solving -1 + -4x2 + 2x4 = 15 Solving for variable 'x'. Reorder the terms: -1 + -15 + -4x2 + 2x4 = 15 + -15 Combine like terms: -1 + -15 = -16 -16 + -4x2 + 2x4 = 15 + -15 Combine like terms: 15 + -15 = 0 -16 + -4x2 + 2x4 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-8 + -2x2 + x4) = 0 Factor a trinomial. 2((-2 + -1x2)(4 + -1x2)) = 0 Factor a difference between two squares. 2((-2 + -1x2)((2 + x)(2 + -1x))) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + -1x2)' equal to zero and attempt to solve: Simplifying -2 + -1x2 = 0 Solving -2 + -1x2 = 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 + -1x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1x2 = 0 + 2 -1x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -1x2 = 2 Divide each side by '-1'. 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 '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 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 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Subproblem 3
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 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 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Solution
x = {-2, 2}
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