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Simplifying 18k2 + 69k + -12 = 0 Reorder the terms: -12 + 69k + 18k2 = 0 Solving -12 + 69k + 18k2 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '3'. 3(-4 + 23k + 6k2) = 0 Factor a trinomial. 3((-4 + -1k)(1 + -6k)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-4 + -1k)' equal to zero and attempt to solve: Simplifying -4 + -1k = 0 Solving -4 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1k = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1k = 0 + 4 -1k = 0 + 4 Combine like terms: 0 + 4 = 4 -1k = 4 Divide each side by '-1'. k = -4 Simplifying k = -4Subproblem 2
Set the factor '(1 + -6k)' equal to zero and attempt to solve: Simplifying 1 + -6k = 0 Solving 1 + -6k = 0 Move all terms containing k to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -6k = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -6k = 0 + -1 -6k = 0 + -1 Combine like terms: 0 + -1 = -1 -6k = -1 Divide each side by '-6'. k = 0.1666666667 Simplifying k = 0.1666666667Solution
k = {-4, 0.1666666667}
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