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Simplifying 6k2 + 9k + -40 = 2 Reorder the terms: -40 + 9k + 6k2 = 2 Solving -40 + 9k + 6k2 = 2 Solving for variable 'k'. Reorder the terms: -40 + -2 + 9k + 6k2 = 2 + -2 Combine like terms: -40 + -2 = -42 -42 + 9k + 6k2 = 2 + -2 Combine like terms: 2 + -2 = 0 -42 + 9k + 6k2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-14 + 3k + 2k2) = 0 Factor a trinomial. 3((-7 + -2k)(2 + -1k)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-7 + -2k)' equal to zero and attempt to solve: Simplifying -7 + -2k = 0 Solving -7 + -2k = 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 + -2k = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -2k = 0 + 7 -2k = 0 + 7 Combine like terms: 0 + 7 = 7 -2k = 7 Divide each side by '-2'. k = -3.5 Simplifying k = -3.5Subproblem 2
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 = 2Solution
k = {-3.5, 2}
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