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Simplifying 35k2 + 200k + 125 = 0 Reorder the terms: 125 + 200k + 35k2 = 0 Solving 125 + 200k + 35k2 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '5'. 5(25 + 40k + 7k2) = 0 Factor a trinomial. 5((5 + k)(5 + 7k)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(5 + k)' equal to zero and attempt to solve: Simplifying 5 + k = 0 Solving 5 + k = 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 + k = 0 + -5 Combine like terms: 5 + -5 = 0 0 + k = 0 + -5 k = 0 + -5 Combine like terms: 0 + -5 = -5 k = -5 Simplifying k = -5Subproblem 2
Set the factor '(5 + 7k)' equal to zero and attempt to solve: Simplifying 5 + 7k = 0 Solving 5 + 7k = 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 + 7k = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 7k = 0 + -5 7k = 0 + -5 Combine like terms: 0 + -5 = -5 7k = -5 Divide each side by '7'. k = -0.7142857143 Simplifying k = -0.7142857143Solution
k = {-5, -0.7142857143}
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