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Simplifying 30k2 + -54k + 24 = 0 Reorder the terms: 24 + -54k + 30k2 = 0 Solving 24 + -54k + 30k2 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '6'. 6(4 + -9k + 5k2) = 0 Factor a trinomial. 6((4 + -5k)(1 + -1k)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(4 + -5k)' equal to zero and attempt to solve: Simplifying 4 + -5k = 0 Solving 4 + -5k = 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 + -5k = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -5k = 0 + -4 -5k = 0 + -4 Combine like terms: 0 + -4 = -4 -5k = -4 Divide each side by '-5'. k = 0.8 Simplifying k = 0.8Subproblem 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 = 1Solution
k = {0.8, 1}
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