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Simplifying (x + 1)(x + 1) + 9(x + 1) + 18 = 0 Reorder the terms: (1 + x)(x + 1) + 9(x + 1) + 18 = 0 Reorder the terms: (1 + x)(1 + x) + 9(x + 1) + 18 = 0 Multiply (1 + x) * (1 + x) (1(1 + x) + x(1 + x)) + 9(x + 1) + 18 = 0 ((1 * 1 + x * 1) + x(1 + x)) + 9(x + 1) + 18 = 0 ((1 + 1x) + x(1 + x)) + 9(x + 1) + 18 = 0 (1 + 1x + (1 * x + x * x)) + 9(x + 1) + 18 = 0 (1 + 1x + (1x + x2)) + 9(x + 1) + 18 = 0 Combine like terms: 1x + 1x = 2x (1 + 2x + x2) + 9(x + 1) + 18 = 0 Reorder the terms: 1 + 2x + x2 + 9(1 + x) + 18 = 0 1 + 2x + x2 + (1 * 9 + x * 9) + 18 = 0 1 + 2x + x2 + (9 + 9x) + 18 = 0 Reorder the terms: 1 + 9 + 18 + 2x + 9x + x2 = 0 Combine like terms: 1 + 9 = 10 10 + 18 + 2x + 9x + x2 = 0 Combine like terms: 10 + 18 = 28 28 + 2x + 9x + x2 = 0 Combine like terms: 2x + 9x = 11x 28 + 11x + x2 = 0 Solving 28 + 11x + x2 = 0 Solving for variable 'x'. Factor a trinomial. (7 + x)(4 + x) = 0Subproblem 1
Set the factor '(7 + x)' equal to zero and attempt to solve: Simplifying 7 + x = 0 Solving 7 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + x = 0 + -7 x = 0 + -7 Combine like terms: 0 + -7 = -7 x = -7 Simplifying x = -7Subproblem 2
Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 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 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4Solution
x = {-7, -4}
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