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Simplifying (1 + -1x)(1 + x) = 0 Multiply (1 + -1x) * (1 + x) (1(1 + x) + -1x * (1 + x)) = 0 ((1 * 1 + x * 1) + -1x * (1 + x)) = 0 ((1 + 1x) + -1x * (1 + x)) = 0 (1 + 1x + (1 * -1x + x * -1x)) = 0 (1 + 1x + (-1x + -1x2)) = 0 Combine like terms: 1x + -1x = 0 (1 + 0 + -1x2) = 0 (1 + -1x2) = 0 Solving 1 + -1x2 = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x2 = 0 + -1 -1x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -1x2 = -1 Divide each side by '-1'. x2 = 1 Simplifying x2 = 1 Take the square root of each side: x = {-1, 1}
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