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Simplifying 42k2 + 36k + -96 = 0 Reorder the terms: -96 + 36k + 42k2 = 0 Solving -96 + 36k + 42k2 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '6'. 6(-16 + 6k + 7k2) = 0 Factor a trinomial. 6((-2 + -1k)(8 + -7k)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-2 + -1k)' equal to zero and attempt to solve: Simplifying -2 + -1k = 0 Solving -2 + -1k = 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 + -1k = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1k = 0 + 2 -1k = 0 + 2 Combine like terms: 0 + 2 = 2 -1k = 2 Divide each side by '-1'. k = -2 Simplifying k = -2Subproblem 2
Set the factor '(8 + -7k)' equal to zero and attempt to solve: Simplifying 8 + -7k = 0 Solving 8 + -7k = 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 + -7k = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -7k = 0 + -8 -7k = 0 + -8 Combine like terms: 0 + -8 = -8 -7k = -8 Divide each side by '-7'. k = 1.142857143 Simplifying k = 1.142857143Solution
k = {-2, 1.142857143}
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