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Simplifying 5k2 = 200 + 15k Solving 5k2 = 200 + 15k Solving for variable 'k'. Reorder the terms: -200 + -15k + 5k2 = 200 + 15k + -200 + -15k Reorder the terms: -200 + -15k + 5k2 = 200 + -200 + 15k + -15k Combine like terms: 200 + -200 = 0 -200 + -15k + 5k2 = 0 + 15k + -15k -200 + -15k + 5k2 = 15k + -15k Combine like terms: 15k + -15k = 0 -200 + -15k + 5k2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-40 + -3k + k2) = 0 Factor a trinomial. 5((-5 + -1k)(8 + -1k)) = 0 Ignore the factor 5.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 '(8 + -1k)' equal to zero and attempt to solve: Simplifying 8 + -1k = 0 Solving 8 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1k = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1k = 0 + -8 -1k = 0 + -8 Combine like terms: 0 + -8 = -8 -1k = -8 Divide each side by '-1'. k = 8 Simplifying k = 8Solution
k = {-5, 8}
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