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Simplifying 9k = k2 + 18 Reorder the terms: 9k = 18 + k2 Solving 9k = 18 + k2 Solving for variable 'k'. Reorder the terms: -18 + 9k + -1k2 = 18 + k2 + -18 + -1k2 Reorder the terms: -18 + 9k + -1k2 = 18 + -18 + k2 + -1k2 Combine like terms: 18 + -18 = 0 -18 + 9k + -1k2 = 0 + k2 + -1k2 -18 + 9k + -1k2 = k2 + -1k2 Combine like terms: k2 + -1k2 = 0 -18 + 9k + -1k2 = 0 Factor a trinomial. (-6 + k)(3 + -1k) = 0Subproblem 1
Set the factor '(-6 + k)' equal to zero and attempt to solve: Simplifying -6 + k = 0 Solving -6 + k = 0 Move all terms containing k to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + k = 0 + 6 Combine like terms: -6 + 6 = 0 0 + k = 0 + 6 k = 0 + 6 Combine like terms: 0 + 6 = 6 k = 6 Simplifying k = 6Subproblem 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 = {6, 3}
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