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Simplifying (x + 3)(x + 9) = 7 Reorder the terms: (3 + x)(x + 9) = 7 Reorder the terms: (3 + x)(9 + x) = 7 Multiply (3 + x) * (9 + x) (3(9 + x) + x(9 + x)) = 7 ((9 * 3 + x * 3) + x(9 + x)) = 7 ((27 + 3x) + x(9 + x)) = 7 (27 + 3x + (9 * x + x * x)) = 7 (27 + 3x + (9x + x2)) = 7 Combine like terms: 3x + 9x = 12x (27 + 12x + x2) = 7 Solving 27 + 12x + x2 = 7 Solving for variable 'x'. Reorder the terms: 27 + -7 + 12x + x2 = 7 + -7 Combine like terms: 27 + -7 = 20 20 + 12x + x2 = 7 + -7 Combine like terms: 7 + -7 = 0 20 + 12x + x2 = 0 Factor a trinomial. (10 + x)(2 + 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 '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 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 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Solution
x = {-10, -2}
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