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Simplifying 4k2 + -62k + 30 = 0 Reorder the terms: 30 + -62k + 4k2 = 0 Solving 30 + -62k + 4k2 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '2'. 2(15 + -31k + 2k2) = 0 Factor a trinomial. 2((1 + -2k)(15 + -1k)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + -2k)' equal to zero and attempt to solve: Simplifying 1 + -2k = 0 Solving 1 + -2k = 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 + -2k = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2k = 0 + -1 -2k = 0 + -1 Combine like terms: 0 + -1 = -1 -2k = -1 Divide each side by '-2'. k = 0.5 Simplifying k = 0.5Subproblem 2
Set the factor '(15 + -1k)' equal to zero and attempt to solve: Simplifying 15 + -1k = 0 Solving 15 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + -1k = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -1k = 0 + -15 -1k = 0 + -15 Combine like terms: 0 + -15 = -15 -1k = -15 Divide each side by '-1'. k = 15 Simplifying k = 15Solution
k = {0.5, 15}
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