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Simplifying (k + -5)(k + -10) = 0 Reorder the terms: (-5 + k)(k + -10) = 0 Reorder the terms: (-5 + k)(-10 + k) = 0 Multiply (-5 + k) * (-10 + k) (-5(-10 + k) + k(-10 + k)) = 0 ((-10 * -5 + k * -5) + k(-10 + k)) = 0 ((50 + -5k) + k(-10 + k)) = 0 (50 + -5k + (-10 * k + k * k)) = 0 (50 + -5k + (-10k + k2)) = 0 Combine like terms: -5k + -10k = -15k (50 + -15k + k2) = 0 Solving 50 + -15k + k2 = 0 Solving for variable 'k'. 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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