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Simplifying 9k2 + 12k = 45 Reorder the terms: 12k + 9k2 = 45 Solving 12k + 9k2 = 45 Solving for variable 'k'. Reorder the terms: -45 + 12k + 9k2 = 45 + -45 Combine like terms: 45 + -45 = 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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