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Simplifying 42k2 + 318k + -540 = 0 Reorder the terms: -540 + 318k + 42k2 = 0 Solving -540 + 318k + 42k2 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '6'. 6(-90 + 53k + 7k2) = 0 Factor a trinomial. 6((-9 + -1k)(10 + -7k)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-9 + -1k)' equal to zero and attempt to solve: Simplifying -9 + -1k = 0 Solving -9 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -1k = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1k = 0 + 9 -1k = 0 + 9 Combine like terms: 0 + 9 = 9 -1k = 9 Divide each side by '-1'. k = -9 Simplifying k = -9Subproblem 2
Set the factor '(10 + -7k)' equal to zero and attempt to solve: Simplifying 10 + -7k = 0 Solving 10 + -7k = 0 Move all terms containing k to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -7k = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -7k = 0 + -10 -7k = 0 + -10 Combine like terms: 0 + -10 = -10 -7k = -10 Divide each side by '-7'. k = 1.428571429 Simplifying k = 1.428571429Solution
k = {-9, 1.428571429}
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