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Simplifying k2 = -50 + 15k Solving k2 = -50 + 15k Solving for variable 'k'. Reorder the terms: 50 + -15k + k2 = -50 + 15k + 50 + -15k Reorder the terms: 50 + -15k + k2 = -50 + 50 + 15k + -15k Combine like terms: -50 + 50 = 0 50 + -15k + k2 = 0 + 15k + -15k 50 + -15k + k2 = 15k + -15k Combine like terms: 15k + -15k = 0 50 + -15k + k2 = 0 Factor a trinomial. (5 + -1k)(10 + -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 '(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 = {5, 10}
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