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Simplifying (2k + 4)(2k + 9) = 0 Reorder the terms: (4 + 2k)(2k + 9) = 0 Reorder the terms: (4 + 2k)(9 + 2k) = 0 Multiply (4 + 2k) * (9 + 2k) (4(9 + 2k) + 2k * (9 + 2k)) = 0 ((9 * 4 + 2k * 4) + 2k * (9 + 2k)) = 0 ((36 + 8k) + 2k * (9 + 2k)) = 0 (36 + 8k + (9 * 2k + 2k * 2k)) = 0 (36 + 8k + (18k + 4k2)) = 0 Combine like terms: 8k + 18k = 26k (36 + 26k + 4k2) = 0 Solving 36 + 26k + 4k2 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '2'. 2(18 + 13k + 2k2) = 0 Factor a trinomial. 2((9 + 2k)(2 + k)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(9 + 2k)' equal to zero and attempt to solve: Simplifying 9 + 2k = 0 Solving 9 + 2k = 0 Move all terms containing k to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + 2k = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 2k = 0 + -9 2k = 0 + -9 Combine like terms: 0 + -9 = -9 2k = -9 Divide each side by '2'. k = -4.5 Simplifying k = -4.5Subproblem 2
Set the factor '(2 + k)' equal to zero and attempt to solve: Simplifying 2 + k = 0 Solving 2 + k = 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 + k = 0 + -2 Combine like terms: 2 + -2 = 0 0 + k = 0 + -2 k = 0 + -2 Combine like terms: 0 + -2 = -2 k = -2 Simplifying k = -2Solution
k = {-4.5, -2}
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