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Simplifying 21k2 + 57k + -18 = 0 Reorder the terms: -18 + 57k + 21k2 = 0 Solving -18 + 57k + 21k2 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '3'. 3(-6 + 19k + 7k2) = 0 Factor a trinomial. 3((-3 + -1k)(2 + -7k)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-3 + -1k)' equal to zero and attempt to solve: Simplifying -3 + -1k = 0 Solving -3 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1k = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1k = 0 + 3 -1k = 0 + 3 Combine like terms: 0 + 3 = 3 -1k = 3 Divide each side by '-1'. k = -3 Simplifying k = -3Subproblem 2
Set the factor '(2 + -7k)' equal to zero and attempt to solve: Simplifying 2 + -7k = 0 Solving 2 + -7k = 0 Move all terms containing k to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -7k = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -7k = 0 + -2 -7k = 0 + -2 Combine like terms: 0 + -2 = -2 -7k = -2 Divide each side by '-7'. k = 0.2857142857 Simplifying k = 0.2857142857Solution
k = {-3, 0.2857142857}
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