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Simplifying (3k + 7)(k + 7) = 0 Reorder the terms: (7 + 3k)(k + 7) = 0 Reorder the terms: (7 + 3k)(7 + k) = 0 Multiply (7 + 3k) * (7 + k) (7(7 + k) + 3k * (7 + k)) = 0 ((7 * 7 + k * 7) + 3k * (7 + k)) = 0 ((49 + 7k) + 3k * (7 + k)) = 0 (49 + 7k + (7 * 3k + k * 3k)) = 0 (49 + 7k + (21k + 3k2)) = 0 Combine like terms: 7k + 21k = 28k (49 + 28k + 3k2) = 0 Solving 49 + 28k + 3k2 = 0 Solving for variable 'k'. Factor a trinomial. (7 + k)(7 + 3k) = 0Subproblem 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 '(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 = -2.333333333Solution
k = {-7, -2.333333333}
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