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Simplifying 8k2 = 16k + 24 Reorder the terms: 8k2 = 24 + 16k Solving 8k2 = 24 + 16k Solving for variable 'k'. Reorder the terms: -24 + -16k + 8k2 = 24 + 16k + -24 + -16k Reorder the terms: -24 + -16k + 8k2 = 24 + -24 + 16k + -16k Combine like terms: 24 + -24 = 0 -24 + -16k + 8k2 = 0 + 16k + -16k -24 + -16k + 8k2 = 16k + -16k Combine like terms: 16k + -16k = 0 -24 + -16k + 8k2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(-3 + -2k + k2) = 0 Factor a trinomial. 8((-1 + -1k)(3 + -1k)) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-1 + -1k)' equal to zero and attempt to solve: Simplifying -1 + -1k = 0 Solving -1 + -1k = 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 + -1k = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1k = 0 + 1 -1k = 0 + 1 Combine like terms: 0 + 1 = 1 -1k = 1 Divide each side by '-1'. k = -1 Simplifying k = -1Subproblem 2
Set the factor '(3 + -1k)' equal to zero and attempt to solve: Simplifying 3 + -1k = 0 Solving 3 + -1k = 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 + -1k = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1k = 0 + -3 -1k = 0 + -3 Combine like terms: 0 + -3 = -3 -1k = -3 Divide each side by '-1'. k = 3 Simplifying k = 3Solution
k = {-1, 3}
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