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Simplifying k2 + 6k + -65 = -10 Reorder the terms: -65 + 6k + k2 = -10 Solving -65 + 6k + k2 = -10 Solving for variable 'k'. Reorder the terms: -65 + 10 + 6k + k2 = -10 + 10 Combine like terms: -65 + 10 = -55 -55 + 6k + k2 = -10 + 10 Combine like terms: -10 + 10 = 0 -55 + 6k + k2 = 0 Factor a trinomial. (-11 + -1k)(5 + -1k) = 0Subproblem 1
Set the factor '(-11 + -1k)' equal to zero and attempt to solve: Simplifying -11 + -1k = 0 Solving -11 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + -1k = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -1k = 0 + 11 -1k = 0 + 11 Combine like terms: 0 + 11 = 11 -1k = 11 Divide each side by '-1'. k = -11 Simplifying k = -11Subproblem 2
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 = 5Solution
k = {-11, 5}
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