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Simplifying 6k2 + 40k = 64 Reorder the terms: 40k + 6k2 = 64 Solving 40k + 6k2 = 64 Solving for variable 'k'. Reorder the terms: -64 + 40k + 6k2 = 64 + -64 Combine like terms: 64 + -64 = 0 -64 + 40k + 6k2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-32 + 20k + 3k2) = 0 Factor a trinomial. 2((-8 + -1k)(4 + -3k)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-8 + -1k)' equal to zero and attempt to solve: Simplifying -8 + -1k = 0 Solving -8 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -1k = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1k = 0 + 8 -1k = 0 + 8 Combine like terms: 0 + 8 = 8 -1k = 8 Divide each side by '-1'. k = -8 Simplifying k = -8Subproblem 2
Set the factor '(4 + -3k)' equal to zero and attempt to solve: Simplifying 4 + -3k = 0 Solving 4 + -3k = 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 + -3k = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3k = 0 + -4 -3k = 0 + -4 Combine like terms: 0 + -4 = -4 -3k = -4 Divide each side by '-3'. k = 1.333333333 Simplifying k = 1.333333333Solution
k = {-8, 1.333333333}
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