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Simplifying 5k2 + -4k + -14 = -5 Reorder the terms: -14 + -4k + 5k2 = -5 Solving -14 + -4k + 5k2 = -5 Solving for variable 'k'. Reorder the terms: -14 + 5 + -4k + 5k2 = -5 + 5 Combine like terms: -14 + 5 = -9 -9 + -4k + 5k2 = -5 + 5 Combine like terms: -5 + 5 = 0 -9 + -4k + 5k2 = 0 Factor a trinomial. (-1 + -1k)(9 + -5k) = 0Subproblem 1
Set the factor '(-1 + -1k)' equal to zero and attempt to solve: Simplifying -1 + -1k = 0 Solving -1 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1k = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1k = 0 + 1 -1k = 0 + 1 Combine like terms: 0 + 1 = 1 -1k = 1 Divide each side by '-1'. k = -1 Simplifying k = -1Subproblem 2
Set the factor '(9 + -5k)' equal to zero and attempt to solve: Simplifying 9 + -5k = 0 Solving 9 + -5k = 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 + -5k = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -5k = 0 + -9 -5k = 0 + -9 Combine like terms: 0 + -9 = -9 -5k = -9 Divide each side by '-5'. k = 1.8 Simplifying k = 1.8Solution
k = {-1, 1.8}
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