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Simplifying (9b + 11)(b + 9) = 79 Reorder the terms: (11 + 9b)(b + 9) = 79 Reorder the terms: (11 + 9b)(9 + b) = 79 Multiply (11 + 9b) * (9 + b) (11(9 + b) + 9b * (9 + b)) = 79 ((9 * 11 + b * 11) + 9b * (9 + b)) = 79 ((99 + 11b) + 9b * (9 + b)) = 79 (99 + 11b + (9 * 9b + b * 9b)) = 79 (99 + 11b + (81b + 9b2)) = 79 Combine like terms: 11b + 81b = 92b (99 + 92b + 9b2) = 79 Solving 99 + 92b + 9b2 = 79 Solving for variable 'b'. Reorder the terms: 99 + -79 + 92b + 9b2 = 79 + -79 Combine like terms: 99 + -79 = 20 20 + 92b + 9b2 = 79 + -79 Combine like terms: 79 + -79 = 0 20 + 92b + 9b2 = 0 Factor a trinomial. (10 + b)(2 + 9b) = 0Subproblem 1
Set the factor '(10 + b)' equal to zero and attempt to solve: Simplifying 10 + b = 0 Solving 10 + b = 0 Move all terms containing b to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + b = 0 + -10 Combine like terms: 10 + -10 = 0 0 + b = 0 + -10 b = 0 + -10 Combine like terms: 0 + -10 = -10 b = -10 Simplifying b = -10Subproblem 2
Set the factor '(2 + 9b)' equal to zero and attempt to solve: Simplifying 2 + 9b = 0 Solving 2 + 9b = 0 Move all terms containing b to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 9b = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 9b = 0 + -2 9b = 0 + -2 Combine like terms: 0 + -2 = -2 9b = -2 Divide each side by '9'. b = -0.2222222222 Simplifying b = -0.2222222222Solution
b = {-10, -0.2222222222}
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