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Simplifying (3k + 2)(3k + 2) = 16 Reorder the terms: (2 + 3k)(3k + 2) = 16 Reorder the terms: (2 + 3k)(2 + 3k) = 16 Multiply (2 + 3k) * (2 + 3k) (2(2 + 3k) + 3k * (2 + 3k)) = 16 ((2 * 2 + 3k * 2) + 3k * (2 + 3k)) = 16 ((4 + 6k) + 3k * (2 + 3k)) = 16 (4 + 6k + (2 * 3k + 3k * 3k)) = 16 (4 + 6k + (6k + 9k2)) = 16 Combine like terms: 6k + 6k = 12k (4 + 12k + 9k2) = 16 Solving 4 + 12k + 9k2 = 16 Solving for variable 'k'. Reorder the terms: 4 + -16 + 12k + 9k2 = 16 + -16 Combine like terms: 4 + -16 = -12 -12 + 12k + 9k2 = 16 + -16 Combine like terms: 16 + -16 = 0 -12 + 12k + 9k2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-4 + 4k + 3k2) = 0 Factor a trinomial. 3((-2 + -1k)(2 + -3k)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-2 + -1k)' equal to zero and attempt to solve: Simplifying -2 + -1k = 0 Solving -2 + -1k = 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 + -1k = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1k = 0 + 2 -1k = 0 + 2 Combine like terms: 0 + 2 = 2 -1k = 2 Divide each side by '-1'. k = -2 Simplifying k = -2Subproblem 2
Set the factor '(2 + -3k)' equal to zero and attempt to solve: Simplifying 2 + -3k = 0 Solving 2 + -3k = 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 + -3k = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3k = 0 + -2 -3k = 0 + -2 Combine like terms: 0 + -2 = -2 -3k = -2 Divide each side by '-3'. k = 0.6666666667 Simplifying k = 0.6666666667Solution
k = {-2, 0.6666666667}
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