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Simplifying x4 + -1x2 = x2 + 8 Reorder the terms: -1x2 + x4 = x2 + 8 Reorder the terms: -1x2 + x4 = 8 + x2 Solving -1x2 + x4 = 8 + x2 Solving for variable 'x'. Reorder the terms: -8 + -1x2 + -1x2 + x4 = 8 + x2 + -8 + -1x2 Combine like terms: -1x2 + -1x2 = -2x2 -8 + -2x2 + x4 = 8 + x2 + -8 + -1x2 Reorder the terms: -8 + -2x2 + x4 = 8 + -8 + x2 + -1x2 Combine like terms: 8 + -8 = 0 -8 + -2x2 + x4 = 0 + x2 + -1x2 -8 + -2x2 + x4 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -8 + -2x2 + x4 = 0 Factor a trinomial. (-2 + -1x2)(4 + -1x2) = 0 Factor a difference between two squares. (-2 + -1x2)((2 + x)(2 + -1x)) = 0Subproblem 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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