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Simplifying 4k2 = 10k + 24 Reorder the terms: 4k2 = 24 + 10k Solving 4k2 = 24 + 10k Solving for variable 'k'. Reorder the terms: -24 + -10k + 4k2 = 24 + 10k + -24 + -10k Reorder the terms: -24 + -10k + 4k2 = 24 + -24 + 10k + -10k Combine like terms: 24 + -24 = 0 -24 + -10k + 4k2 = 0 + 10k + -10k -24 + -10k + 4k2 = 10k + -10k Combine like terms: 10k + -10k = 0 -24 + -10k + 4k2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-12 + -5k + 2k2) = 0 Factor a trinomial. 2((-3 + -2k)(4 + -1k)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + -2k)' equal to zero and attempt to solve: Simplifying -3 + -2k = 0 Solving -3 + -2k = 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 + -2k = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2k = 0 + 3 -2k = 0 + 3 Combine like terms: 0 + 3 = 3 -2k = 3 Divide each side by '-2'. k = -1.5 Simplifying k = -1.5Subproblem 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 = {-1.5, 4}
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