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Simplifying 48k2 + -222k + 120 = 0 Reorder the terms: 120 + -222k + 48k2 = 0 Solving 120 + -222k + 48k2 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '6'. 6(20 + -37k + 8k2) = 0 Factor a trinomial. 6((5 + -8k)(4 + -1k)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(5 + -8k)' equal to zero and attempt to solve: Simplifying 5 + -8k = 0 Solving 5 + -8k = 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 + -8k = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -8k = 0 + -5 -8k = 0 + -5 Combine like terms: 0 + -5 = -5 -8k = -5 Divide each side by '-8'. k = 0.625 Simplifying k = 0.625Subproblem 2
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 = 4Solution
k = {0.625, 4}
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