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Simplifying (x + 6)(x + 6) + 7(x + 6) + 12 = 0 Reorder the terms: (6 + x)(x + 6) + 7(x + 6) + 12 = 0 Reorder the terms: (6 + x)(6 + x) + 7(x + 6) + 12 = 0 Multiply (6 + x) * (6 + x) (6(6 + x) + x(6 + x)) + 7(x + 6) + 12 = 0 ((6 * 6 + x * 6) + x(6 + x)) + 7(x + 6) + 12 = 0 ((36 + 6x) + x(6 + x)) + 7(x + 6) + 12 = 0 (36 + 6x + (6 * x + x * x)) + 7(x + 6) + 12 = 0 (36 + 6x + (6x + x2)) + 7(x + 6) + 12 = 0 Combine like terms: 6x + 6x = 12x (36 + 12x + x2) + 7(x + 6) + 12 = 0 Reorder the terms: 36 + 12x + x2 + 7(6 + x) + 12 = 0 36 + 12x + x2 + (6 * 7 + x * 7) + 12 = 0 36 + 12x + x2 + (42 + 7x) + 12 = 0 Reorder the terms: 36 + 42 + 12 + 12x + 7x + x2 = 0 Combine like terms: 36 + 42 = 78 78 + 12 + 12x + 7x + x2 = 0 Combine like terms: 78 + 12 = 90 90 + 12x + 7x + x2 = 0 Combine like terms: 12x + 7x = 19x 90 + 19x + x2 = 0 Solving 90 + 19x + x2 = 0 Solving for variable 'x'. Factor a trinomial. (10 + x)(9 + x) = 0Subproblem 1
Set the factor '(10 + x)' equal to zero and attempt to solve: Simplifying 10 + x = 0 Solving 10 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + x = 0 + -10 x = 0 + -10 Combine like terms: 0 + -10 = -10 x = -10 Simplifying x = -10Subproblem 2
Set the factor '(9 + x)' equal to zero and attempt to solve: Simplifying 9 + x = 0 Solving 9 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + x = 0 + -9 x = 0 + -9 Combine like terms: 0 + -9 = -9 x = -9 Simplifying x = -9Solution
x = {-10, -9}
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