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Simplifying x4 + -60 + 2x2 = -2x4 + -1x2 Reorder the terms: -60 + 2x2 + x4 = -2x4 + -1x2 Reorder the terms: -60 + 2x2 + x4 = -1x2 + -2x4 Solving -60 + 2x2 + x4 = -1x2 + -2x4 Solving for variable 'x'. Reorder the terms: -60 + 2x2 + x2 + x4 + 2x4 = -1x2 + -2x4 + x2 + 2x4 Combine like terms: 2x2 + x2 = 3x2 -60 + 3x2 + x4 + 2x4 = -1x2 + -2x4 + x2 + 2x4 Combine like terms: x4 + 2x4 = 3x4 -60 + 3x2 + 3x4 = -1x2 + -2x4 + x2 + 2x4 Reorder the terms: -60 + 3x2 + 3x4 = -1x2 + x2 + -2x4 + 2x4 Combine like terms: -1x2 + x2 = 0 -60 + 3x2 + 3x4 = 0 + -2x4 + 2x4 -60 + 3x2 + 3x4 = -2x4 + 2x4 Combine like terms: -2x4 + 2x4 = 0 -60 + 3x2 + 3x4 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-20 + x2 + x4) = 0 Factor a trinomial. 3((-5 + -1x2)(4 + -1x2)) = 0 Factor a difference between two squares. 3((-5 + -1x2)((2 + x)(2 + -1x))) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-5 + -1x2)' equal to zero and attempt to solve: Simplifying -5 + -1x2 = 0 Solving -5 + -1x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1x2 = 0 + 5 -1x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -1x2 = 5 Divide each side by '-1'. x2 = -5 Simplifying x2 = -5 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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