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