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Simplifying (9k + 11)(k + 9) = 79 Reorder the terms: (11 + 9k)(k + 9) = 79 Reorder the terms: (11 + 9k)(9 + k) = 79 Multiply (11 + 9k) * (9 + k) (11(9 + k) + 9k * (9 + k)) = 79 ((9 * 11 + k * 11) + 9k * (9 + k)) = 79 ((99 + 11k) + 9k * (9 + k)) = 79 (99 + 11k + (9 * 9k + k * 9k)) = 79 (99 + 11k + (81k + 9k2)) = 79 Combine like terms: 11k + 81k = 92k (99 + 92k + 9k2) = 79 Solving 99 + 92k + 9k2 = 79 Solving for variable 'k'. Reorder the terms: 99 + -79 + 92k + 9k2 = 79 + -79 Combine like terms: 99 + -79 = 20 20 + 92k + 9k2 = 79 + -79 Combine like terms: 79 + -79 = 0 20 + 92k + 9k2 = 0 Factor a trinomial. (10 + k)(2 + 9k) = 0Subproblem 1
Set the factor '(10 + k)' equal to zero and attempt to solve: Simplifying 10 + k = 0 Solving 10 + k = 0 Move all terms containing k to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + k = 0 + -10 Combine like terms: 10 + -10 = 0 0 + k = 0 + -10 k = 0 + -10 Combine like terms: 0 + -10 = -10 k = -10 Simplifying k = -10Subproblem 2
Set the factor '(2 + 9k)' equal to zero and attempt to solve: Simplifying 2 + 9k = 0 Solving 2 + 9k = 0 Move all terms containing k to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 9k = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 9k = 0 + -2 9k = 0 + -2 Combine like terms: 0 + -2 = -2 9k = -2 Divide each side by '9'. k = -0.2222222222 Simplifying k = -0.2222222222Solution
k = {-10, -0.2222222222}
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