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Simplifying 0 = -2x4 + 16x2 + -32 Reorder the terms: 0 = -32 + 16x2 + -2x4 Solving 0 = -32 + 16x2 + -2x4 Solving for variable 'x'. Combine like terms: 0 + 32 = 32 32 + -16x2 + 2x4 = -32 + 16x2 + -2x4 + 32 + -16x2 + 2x4 Reorder the terms: 32 + -16x2 + 2x4 = -32 + 32 + 16x2 + -16x2 + -2x4 + 2x4 Combine like terms: -32 + 32 = 0 32 + -16x2 + 2x4 = 0 + 16x2 + -16x2 + -2x4 + 2x4 32 + -16x2 + 2x4 = 16x2 + -16x2 + -2x4 + 2x4 Combine like terms: 16x2 + -16x2 = 0 32 + -16x2 + 2x4 = 0 + -2x4 + 2x4 32 + -16x2 + 2x4 = -2x4 + 2x4 Combine like terms: -2x4 + 2x4 = 0 32 + -16x2 + 2x4 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(16 + -8x2 + x4) = 0 Factor a trinomial. 2((4 + -1x2)(4 + -1x2)) = 0 Factor a difference between two squares. 2(((2 + x)(2 + -1x))(4 + -1x2)) = 0 Factor a difference between two squares. 2(((2 + x)(2 + -1x))(2 + x)(2 + -1x)) = 0 Ignore the factor 2.Subproblem 1
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 2
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 = 2Subproblem 3
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 4
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, -2, 2}
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