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Simplifying 13k = 2k2 + 18 Reorder the terms: 13k = 18 + 2k2 Solving 13k = 18 + 2k2 Solving for variable 'k'. Reorder the terms: -18 + 13k + -2k2 = 18 + 2k2 + -18 + -2k2 Reorder the terms: -18 + 13k + -2k2 = 18 + -18 + 2k2 + -2k2 Combine like terms: 18 + -18 = 0 -18 + 13k + -2k2 = 0 + 2k2 + -2k2 -18 + 13k + -2k2 = 2k2 + -2k2 Combine like terms: 2k2 + -2k2 = 0 -18 + 13k + -2k2 = 0 Factor a trinomial. (-9 + 2k)(2 + -1k) = 0Subproblem 1
Set the factor '(-9 + 2k)' equal to zero and attempt to solve: Simplifying -9 + 2k = 0 Solving -9 + 2k = 0 Move all terms containing k to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + 2k = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 2k = 0 + 9 2k = 0 + 9 Combine like terms: 0 + 9 = 9 2k = 9 Divide each side by '2'. k = 4.5 Simplifying k = 4.5Subproblem 2
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 = 2Solution
k = {4.5, 2}
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