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Simplifying 6k2 + 54k = -84 Reorder the terms: 54k + 6k2 = -84 Solving 54k + 6k2 = -84 Solving for variable 'k'. Reorder the terms: 84 + 54k + 6k2 = -84 + 84 Combine like terms: -84 + 84 = 0 84 + 54k + 6k2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(14 + 9k + k2) = 0 Factor a trinomial. 6((7 + k)(2 + k)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(7 + k)' equal to zero and attempt to solve: Simplifying 7 + k = 0 Solving 7 + k = 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 + k = 0 + -7 Combine like terms: 7 + -7 = 0 0 + k = 0 + -7 k = 0 + -7 Combine like terms: 0 + -7 = -7 k = -7 Simplifying k = -7Subproblem 2
Set the factor '(2 + k)' equal to zero and attempt to solve: Simplifying 2 + k = 0 Solving 2 + k = 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 + k = 0 + -2 Combine like terms: 2 + -2 = 0 0 + k = 0 + -2 k = 0 + -2 Combine like terms: 0 + -2 = -2 k = -2 Simplifying k = -2Solution
k = {-7, -2}
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