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Simplifying k2 + -6k + 17 = 9 Reorder the terms: 17 + -6k + k2 = 9 Solving 17 + -6k + k2 = 9 Solving for variable 'k'. Reorder the terms: 17 + -9 + -6k + k2 = 9 + -9 Combine like terms: 17 + -9 = 8 8 + -6k + k2 = 9 + -9 Combine like terms: 9 + -9 = 0 8 + -6k + k2 = 0 Factor a trinomial. (2 + -1k)(4 + -1k) = 0Subproblem 1
Set the factor '(2 + -1k)' equal to zero and attempt to solve: Simplifying 2 + -1k = 0 Solving 2 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1k = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1k = 0 + -2 -1k = 0 + -2 Combine like terms: 0 + -2 = -2 -1k = -2 Divide each side by '-1'. k = 2 Simplifying k = 2Subproblem 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 = {2, 4}
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