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Simplifying x(x + 1) = x + (x + 1) + 1 Reorder the terms: x(1 + x) = x + (x + 1) + 1 (1 * x + x * x) = x + (x + 1) + 1 (1x + x2) = x + (x + 1) + 1 Reorder the terms: 1x + x2 = x + (1 + x) + 1 Remove parenthesis around (1 + x) 1x + x2 = x + 1 + x + 1 Reorder the terms: 1x + x2 = 1 + 1 + x + x Combine like terms: 1 + 1 = 2 1x + x2 = 2 + x + x Combine like terms: x + x = 2x 1x + x2 = 2 + 2x Solving 1x + x2 = 2 + 2x Solving for variable 'x'. Reorder the terms: -2 + 1x + -2x + x2 = 2 + 2x + -2 + -2x Combine like terms: 1x + -2x = -1x -2 + -1x + x2 = 2 + 2x + -2 + -2x Reorder the terms: -2 + -1x + x2 = 2 + -2 + 2x + -2x Combine like terms: 2 + -2 = 0 -2 + -1x + x2 = 0 + 2x + -2x -2 + -1x + x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -2 + -1x + x2 = 0 Factor a trinomial. (-1 + -1x)(2 + -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 '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 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 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Solution
x = {-1, 2}
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