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Simplifying 14k2 + 38k = 12 Reorder the terms: 38k + 14k2 = 12 Solving 38k + 14k2 = 12 Solving for variable 'k'. Reorder the terms: -12 + 38k + 14k2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + 38k + 14k2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-6 + 19k + 7k2) = 0 Factor a trinomial. 2((-3 + -1k)(2 + -7k)) = 0 Ignore the factor 2.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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