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Simplifying 24k2 + -31k + -36 = -1k Reorder the terms: -36 + -31k + 24k2 = -1k Solving -36 + -31k + 24k2 = -1k Solving for variable 'k'. Reorder the terms: -36 + -31k + k + 24k2 = -1k + k Combine like terms: -31k + k = -30k -36 + -30k + 24k2 = -1k + k Combine like terms: -1k + k = 0 -36 + -30k + 24k2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-6 + -5k + 4k2) = 0 Factor a trinomial. 6((-3 + -4k)(2 + -1k)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-3 + -4k)' equal to zero and attempt to solve: Simplifying -3 + -4k = 0 Solving -3 + -4k = 0 Move all terms containing k to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -4k = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4k = 0 + 3 -4k = 0 + 3 Combine like terms: 0 + 3 = 3 -4k = 3 Divide each side by '-4'. k = -0.75 Simplifying k = -0.75Subproblem 2
Set the factor '(2 + -1k)' equal to zero and attempt to solve: Simplifying 2 + -1k = 0 Solving 2 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1k = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1k = 0 + -2 -1k = 0 + -2 Combine like terms: 0 + -2 = -2 -1k = -2 Divide each side by '-1'. k = 2 Simplifying k = 2Solution
k = {-0.75, 2}
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