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Simplifying 7k2 + -28k + -84 = 0 Reorder the terms: -84 + -28k + 7k2 = 0 Solving -84 + -28k + 7k2 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '7'. 7(-12 + -4k + k2) = 0 Factor a trinomial. 7((-2 + -1k)(6 + -1k)) = 0 Ignore the factor 7.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 '(6 + -1k)' equal to zero and attempt to solve: Simplifying 6 + -1k = 0 Solving 6 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1k = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1k = 0 + -6 -1k = 0 + -6 Combine like terms: 0 + -6 = -6 -1k = -6 Divide each side by '-1'. k = 6 Simplifying k = 6Solution
k = {-2, 6}
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