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Simplifying -18k3 + -48k2 + 66k = 0 Reorder the terms: 66k + -48k2 + -18k3 = 0 Solving 66k + -48k2 + -18k3 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '6k'. 6k(11 + -8k + -3k2) = 0 Factor a trinomial. 6k((1 + -1k)(11 + 3k)) = 0 Ignore the factor 6.Subproblem 1
Set the factor 'k' equal to zero and attempt to solve: Simplifying k = 0 Solving k = 0 Move all terms containing k to the left, all other terms to the right. Simplifying k = 0Subproblem 2
Set the factor '(1 + -1k)' equal to zero and attempt to solve: Simplifying 1 + -1k = 0 Solving 1 + -1k = 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 + -1k = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1k = 0 + -1 -1k = 0 + -1 Combine like terms: 0 + -1 = -1 -1k = -1 Divide each side by '-1'. k = 1 Simplifying k = 1Subproblem 3
Set the factor '(11 + 3k)' equal to zero and attempt to solve: Simplifying 11 + 3k = 0 Solving 11 + 3k = 0 Move all terms containing k to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + 3k = 0 + -11 Combine like terms: 11 + -11 = 0 0 + 3k = 0 + -11 3k = 0 + -11 Combine like terms: 0 + -11 = -11 3k = -11 Divide each side by '3'. k = -3.666666667 Simplifying k = -3.666666667Solution
k = {0, 1, -3.666666667}
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