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Simplifying (3k + 2)(3k + 2) = 49 Reorder the terms: (2 + 3k)(3k + 2) = 49 Reorder the terms: (2 + 3k)(2 + 3k) = 49 Multiply (2 + 3k) * (2 + 3k) (2(2 + 3k) + 3k * (2 + 3k)) = 49 ((2 * 2 + 3k * 2) + 3k * (2 + 3k)) = 49 ((4 + 6k) + 3k * (2 + 3k)) = 49 (4 + 6k + (2 * 3k + 3k * 3k)) = 49 (4 + 6k + (6k + 9k2)) = 49 Combine like terms: 6k + 6k = 12k (4 + 12k + 9k2) = 49 Solving 4 + 12k + 9k2 = 49 Solving for variable 'k'. Reorder the terms: 4 + -49 + 12k + 9k2 = 49 + -49 Combine like terms: 4 + -49 = -45 -45 + 12k + 9k2 = 49 + -49 Combine like terms: 49 + -49 = 0 -45 + 12k + 9k2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-15 + 4k + 3k2) = 0 Factor a trinomial. 3((-3 + -1k)(5 + -3k)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-3 + -1k)' equal to zero and attempt to solve: Simplifying -3 + -1k = 0 Solving -3 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1k = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1k = 0 + 3 -1k = 0 + 3 Combine like terms: 0 + 3 = 3 -1k = 3 Divide each side by '-1'. k = -3 Simplifying k = -3Subproblem 2
Set the factor '(5 + -3k)' equal to zero and attempt to solve: Simplifying 5 + -3k = 0 Solving 5 + -3k = 0 Move all terms containing k to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -3k = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3k = 0 + -5 -3k = 0 + -5 Combine like terms: 0 + -5 = -5 -3k = -5 Divide each side by '-3'. k = 1.666666667 Simplifying k = 1.666666667Solution
k = {-3, 1.666666667}
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