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Simplifying 42k2 + 234k + -420 = 0 Reorder the terms: -420 + 234k + 42k2 = 0 Solving -420 + 234k + 42k2 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '6'. 6(-70 + 39k + 7k2) = 0 Factor a trinomial. 6((-7 + -1k)(10 + -7k)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-7 + -1k)' equal to zero and attempt to solve: Simplifying -7 + -1k = 0 Solving -7 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -1k = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1k = 0 + 7 -1k = 0 + 7 Combine like terms: 0 + 7 = 7 -1k = 7 Divide each side by '-1'. k = -7 Simplifying k = -7Subproblem 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 = {-7, 1.428571429}
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