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Simplifying 12k2 + 34k + 14 = 0 Reorder the terms: 14 + 34k + 12k2 = 0 Solving 14 + 34k + 12k2 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '2'. 2(7 + 17k + 6k2) = 0 Factor a trinomial. 2((7 + 3k)(1 + 2k)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7 + 3k)' equal to zero and attempt to solve: Simplifying 7 + 3k = 0 Solving 7 + 3k = 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 + 3k = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 3k = 0 + -7 3k = 0 + -7 Combine like terms: 0 + -7 = -7 3k = -7 Divide each side by '3'. k = -2.333333333 Simplifying k = -2.333333333Subproblem 2
Set the factor '(1 + 2k)' equal to zero and attempt to solve: Simplifying 1 + 2k = 0 Solving 1 + 2k = 0 Move all terms containing k to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2k = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2k = 0 + -1 2k = 0 + -1 Combine like terms: 0 + -1 = -1 2k = -1 Divide each side by '2'. k = -0.5 Simplifying k = -0.5Solution
k = {-2.333333333, -0.5}
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