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Simplifying (x + 1)(x + 1) = 9 Reorder the terms: (1 + x)(x + 1) = 9 Reorder the terms: (1 + x)(1 + x) = 9 Multiply (1 + x) * (1 + x) (1(1 + x) + x(1 + x)) = 9 ((1 * 1 + x * 1) + x(1 + x)) = 9 ((1 + 1x) + x(1 + x)) = 9 (1 + 1x + (1 * x + x * x)) = 9 (1 + 1x + (1x + x2)) = 9 Combine like terms: 1x + 1x = 2x (1 + 2x + x2) = 9 Solving 1 + 2x + x2 = 9 Solving for variable 'x'. Reorder the terms: 1 + -9 + 2x + x2 = 9 + -9 Combine like terms: 1 + -9 = -8 -8 + 2x + x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -8 + 2x + x2 = 0 Factor a trinomial. (-4 + -1x)(2 + -1x) = 0Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve: Simplifying -4 + -1x = 0 Solving -4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1x = 0 + 4 -1x = 0 + 4 Combine like terms: 0 + 4 = 4 -1x = 4 Divide each side by '-1'. x = -4 Simplifying x = -4Subproblem 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 = {-4, 2}
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