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Simplifying k2 + 14k + -77 = -5 Reorder the terms: -77 + 14k + k2 = -5 Solving -77 + 14k + k2 = -5 Solving for variable 'k'. Reorder the terms: -77 + 5 + 14k + k2 = -5 + 5 Combine like terms: -77 + 5 = -72 -72 + 14k + k2 = -5 + 5 Combine like terms: -5 + 5 = 0 -72 + 14k + k2 = 0 Factor a trinomial. (-18 + -1k)(4 + -1k) = 0Subproblem 1
Set the factor '(-18 + -1k)' equal to zero and attempt to solve: Simplifying -18 + -1k = 0 Solving -18 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + -1k = 0 + 18 Combine like terms: -18 + 18 = 0 0 + -1k = 0 + 18 -1k = 0 + 18 Combine like terms: 0 + 18 = 18 -1k = 18 Divide each side by '-1'. k = -18 Simplifying k = -18Subproblem 2
Set the factor '(4 + -1k)' equal to zero and attempt to solve: Simplifying 4 + -1k = 0 Solving 4 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1k = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1k = 0 + -4 -1k = 0 + -4 Combine like terms: 0 + -4 = -4 -1k = -4 Divide each side by '-1'. k = 4 Simplifying k = 4Solution
k = {-18, 4}
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