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Simplifying (x2 + -2x + 1)(x2 + 2x + 1) = 0 Reorder the terms: (1 + -2x + x2)(x2 + 2x + 1) = 0 Reorder the terms: (1 + -2x + x2)(1 + 2x + x2) = 0 Multiply (1 + -2x + x2) * (1 + 2x + x2) (1(1 + 2x + x2) + -2x * (1 + 2x + x2) + x2(1 + 2x + x2)) = 0 ((1 * 1 + 2x * 1 + x2 * 1) + -2x * (1 + 2x + x2) + x2(1 + 2x + x2)) = 0 ((1 + 2x + 1x2) + -2x * (1 + 2x + x2) + x2(1 + 2x + x2)) = 0 (1 + 2x + 1x2 + (1 * -2x + 2x * -2x + x2 * -2x) + x2(1 + 2x + x2)) = 0 (1 + 2x + 1x2 + (-2x + -4x2 + -2x3) + x2(1 + 2x + x2)) = 0 (1 + 2x + 1x2 + -2x + -4x2 + -2x3 + (1 * x2 + 2x * x2 + x2 * x2)) = 0 (1 + 2x + 1x2 + -2x + -4x2 + -2x3 + (1x2 + 2x3 + x4)) = 0 Reorder the terms: (1 + 2x + -2x + 1x2 + -4x2 + 1x2 + -2x3 + 2x3 + x4) = 0 Combine like terms: 2x + -2x = 0 (1 + 0 + 1x2 + -4x2 + 1x2 + -2x3 + 2x3 + x4) = 0 (1 + 1x2 + -4x2 + 1x2 + -2x3 + 2x3 + x4) = 0 Combine like terms: 1x2 + -4x2 = -3x2 (1 + -3x2 + 1x2 + -2x3 + 2x3 + x4) = 0 Combine like terms: -3x2 + 1x2 = -2x2 (1 + -2x2 + -2x3 + 2x3 + x4) = 0 Combine like terms: -2x3 + 2x3 = 0 (1 + -2x2 + 0 + x4) = 0 (1 + -2x2 + x4) = 0 Solving 1 + -2x2 + x4 = 0 Solving for variable 'x'. Factor a trinomial. (1 + -1x2)(1 + -1x2) = 0 Factor a difference between two squares. ((1 + x)(1 + -1x))(1 + -1x2) = 0 Factor a difference between two squares. ((1 + x)(1 + -1x))(1 + x)(1 + -1x) = 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 + -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 = 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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