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