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Simplifying 180k2 + 300k + 125 = 0 Reorder the terms: 125 + 300k + 180k2 = 0 Solving 125 + 300k + 180k2 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '5'. 5(25 + 60k + 36k2) = 0 Factor a trinomial. 5((5 + 6k)(5 + 6k)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(5 + 6k)' equal to zero and attempt to solve: Simplifying 5 + 6k = 0 Solving 5 + 6k = 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 + 6k = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 6k = 0 + -5 6k = 0 + -5 Combine like terms: 0 + -5 = -5 6k = -5 Divide each side by '6'. k = -0.8333333333 Simplifying k = -0.8333333333Subproblem 2
Set the factor '(5 + 6k)' equal to zero and attempt to solve: Simplifying 5 + 6k = 0 Solving 5 + 6k = 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 + 6k = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 6k = 0 + -5 6k = 0 + -5 Combine like terms: 0 + -5 = -5 6k = -5 Divide each side by '6'. k = -0.8333333333 Simplifying k = -0.8333333333Solution
k = {-0.8333333333, -0.8333333333}
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