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Simplifying k2 = -30 + 11k Solving k2 = -30 + 11k Solving for variable 'k'. Reorder the terms: 30 + -11k + k2 = -30 + 11k + 30 + -11k Reorder the terms: 30 + -11k + k2 = -30 + 30 + 11k + -11k Combine like terms: -30 + 30 = 0 30 + -11k + k2 = 0 + 11k + -11k 30 + -11k + k2 = 11k + -11k Combine like terms: 11k + -11k = 0 30 + -11k + k2 = 0 Factor a trinomial. (5 + -1k)(6 + -1k) = 0Subproblem 1
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 = 5Subproblem 2
Set the factor '(6 + -1k)' equal to zero and attempt to solve: Simplifying 6 + -1k = 0 Solving 6 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1k = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1k = 0 + -6 -1k = 0 + -6 Combine like terms: 0 + -6 = -6 -1k = -6 Divide each side by '-1'. k = 6 Simplifying k = 6Solution
k = {5, 6}
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