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Simplifying (x + 1)(x + -1) + -2(x + -1) = 0 Reorder the terms: (1 + x)(x + -1) + -2(x + -1) = 0 Reorder the terms: (1 + x)(-1 + x) + -2(x + -1) = 0 Multiply (1 + x) * (-1 + x) (1(-1 + x) + x(-1 + x)) + -2(x + -1) = 0 ((-1 * 1 + x * 1) + x(-1 + x)) + -2(x + -1) = 0 ((-1 + 1x) + x(-1 + x)) + -2(x + -1) = 0 (-1 + 1x + (-1 * x + x * x)) + -2(x + -1) = 0 (-1 + 1x + (-1x + x2)) + -2(x + -1) = 0 Combine like terms: 1x + -1x = 0 (-1 + 0 + x2) + -2(x + -1) = 0 (-1 + x2) + -2(x + -1) = 0 Reorder the terms: -1 + x2 + -2(-1 + x) = 0 -1 + x2 + (-1 * -2 + x * -2) = 0 -1 + x2 + (2 + -2x) = 0 Reorder the terms: -1 + 2 + -2x + x2 = 0 Combine like terms: -1 + 2 = 1 1 + -2x + x2 = 0 Solving 1 + -2x + x2 = 0 Solving for variable 'x'. Factor a trinomial. (1 + -1x)(1 + -1x) = 0Subproblem 1
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 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 = 1Solution
x = {1, 1}
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