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Simplifying k2 + -12k + 27 = -8 Reorder the terms: 27 + -12k + k2 = -8 Solving 27 + -12k + k2 = -8 Solving for variable 'k'. Reorder the terms: 27 + 8 + -12k + k2 = -8 + 8 Combine like terms: 27 + 8 = 35 35 + -12k + k2 = -8 + 8 Combine like terms: -8 + 8 = 0 35 + -12k + k2 = 0 Factor a trinomial. (5 + -1k)(7 + -1k) = 0Subproblem 1
Set the factor '(5 + -1k)' equal to zero and attempt to solve: Simplifying 5 + -1k = 0 Solving 5 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1k = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1k = 0 + -5 -1k = 0 + -5 Combine like terms: 0 + -5 = -5 -1k = -5 Divide each side by '-1'. k = 5 Simplifying k = 5Subproblem 2
Set the factor '(7 + -1k)' equal to zero and attempt to solve: Simplifying 7 + -1k = 0 Solving 7 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1k = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1k = 0 + -7 -1k = 0 + -7 Combine like terms: 0 + -7 = -7 -1k = -7 Divide each side by '-1'. k = 7 Simplifying k = 7Solution
k = {5, 7}
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