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Simplifying 2k2 = 27k + -81 Reorder the terms: 2k2 = -81 + 27k Solving 2k2 = -81 + 27k Solving for variable 'k'. Reorder the terms: 81 + -27k + 2k2 = -81 + 27k + 81 + -27k Reorder the terms: 81 + -27k + 2k2 = -81 + 81 + 27k + -27k Combine like terms: -81 + 81 = 0 81 + -27k + 2k2 = 0 + 27k + -27k 81 + -27k + 2k2 = 27k + -27k Combine like terms: 27k + -27k = 0 81 + -27k + 2k2 = 0 Factor a trinomial. (9 + -2k)(9 + -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 '(9 + -1k)' equal to zero and attempt to solve: Simplifying 9 + -1k = 0 Solving 9 + -1k = 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 + -1k = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1k = 0 + -9 -1k = 0 + -9 Combine like terms: 0 + -9 = -9 -1k = -9 Divide each side by '-1'. k = 9 Simplifying k = 9Solution
k = {4.5, 9}
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