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