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Simplifying 8k2 = 16k + 64 Reorder the terms: 8k2 = 64 + 16k Solving 8k2 = 64 + 16k Solving for variable 'k'. Reorder the terms: -64 + -16k + 8k2 = 64 + 16k + -64 + -16k Reorder the terms: -64 + -16k + 8k2 = 64 + -64 + 16k + -16k Combine like terms: 64 + -64 = 0 -64 + -16k + 8k2 = 0 + 16k + -16k -64 + -16k + 8k2 = 16k + -16k Combine like terms: 16k + -16k = 0 -64 + -16k + 8k2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(-8 + -2k + k2) = 0 Factor a trinomial. 8((-2 + -1k)(4 + -1k)) = 0 Ignore the factor 8.Subproblem 1
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 = -2Subproblem 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 = {-2, 4}
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