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Simplifying 2k2 = 30k + -100 Reorder the terms: 2k2 = -100 + 30k Solving 2k2 = -100 + 30k Solving for variable 'k'. Reorder the terms: 100 + -30k + 2k2 = -100 + 30k + 100 + -30k Reorder the terms: 100 + -30k + 2k2 = -100 + 100 + 30k + -30k Combine like terms: -100 + 100 = 0 100 + -30k + 2k2 = 0 + 30k + -30k 100 + -30k + 2k2 = 30k + -30k Combine like terms: 30k + -30k = 0 100 + -30k + 2k2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(50 + -15k + k2) = 0 Factor a trinomial. 2((5 + -1k)(10 + -1k)) = 0 Ignore the factor 2.Subproblem 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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