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Simplifying 8(8 + -1k) * k = -72k Reorder the terms for easier multiplication: 8k(8 + -1k) = -72k (8 * 8k + -1k * 8k) = -72k (64k + -8k2) = -72k Solving 64k + -8k2 = -72k Solving for variable 'k'. Reorder the terms: 64k + 72k + -8k2 = -72k + 72k Combine like terms: 64k + 72k = 136k 136k + -8k2 = -72k + 72k Combine like terms: -72k + 72k = 0 136k + -8k2 = 0 Factor out the Greatest Common Factor (GCF), '8k'. 8k(17 + -1k) = 0 Ignore the factor 8.Subproblem 1
Set the factor 'k' equal to zero and attempt to solve: Simplifying k = 0 Solving k = 0 Move all terms containing k to the left, all other terms to the right. Simplifying k = 0Subproblem 2
Set the factor '(17 + -1k)' equal to zero and attempt to solve: Simplifying 17 + -1k = 0 Solving 17 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + -1k = 0 + -17 Combine like terms: 17 + -17 = 0 0 + -1k = 0 + -17 -1k = 0 + -17 Combine like terms: 0 + -17 = -17 -1k = -17 Divide each side by '-1'. k = 17 Simplifying k = 17Solution
k = {0, 17}
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