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Simplifying k2 + -18k + 77 = -3 Reorder the terms: 77 + -18k + k2 = -3 Solving 77 + -18k + k2 = -3 Solving for variable 'k'. Reorder the terms: 77 + 3 + -18k + k2 = -3 + 3 Combine like terms: 77 + 3 = 80 80 + -18k + k2 = -3 + 3 Combine like terms: -3 + 3 = 0 80 + -18k + k2 = 0 Factor a trinomial. (8 + -1k)(10 + -1k) = 0Subproblem 1
Set the factor '(8 + -1k)' equal to zero and attempt to solve: Simplifying 8 + -1k = 0 Solving 8 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1k = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1k = 0 + -8 -1k = 0 + -8 Combine like terms: 0 + -8 = -8 -1k = -8 Divide each side by '-1'. k = 8 Simplifying k = 8Subproblem 2
Set the factor '(10 + -1k)' equal to zero and attempt to solve: Simplifying 10 + -1k = 0 Solving 10 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1k = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1k = 0 + -10 -1k = 0 + -10 Combine like terms: 0 + -10 = -10 -1k = -10 Divide each side by '-1'. k = 10 Simplifying k = 10Solution
k = {8, 10}
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