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Simplifying (5k + 7)(k + 1) = 0 Reorder the terms: (7 + 5k)(k + 1) = 0 Reorder the terms: (7 + 5k)(1 + k) = 0 Multiply (7 + 5k) * (1 + k) (7(1 + k) + 5k * (1 + k)) = 0 ((1 * 7 + k * 7) + 5k * (1 + k)) = 0 ((7 + 7k) + 5k * (1 + k)) = 0 (7 + 7k + (1 * 5k + k * 5k)) = 0 (7 + 7k + (5k + 5k2)) = 0 Combine like terms: 7k + 5k = 12k (7 + 12k + 5k2) = 0 Solving 7 + 12k + 5k2 = 0 Solving for variable 'k'. Factor a trinomial. (7 + 5k)(1 + k) = 0Subproblem 1
Set the factor '(7 + 5k)' equal to zero and attempt to solve: Simplifying 7 + 5k = 0 Solving 7 + 5k = 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 + 5k = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 5k = 0 + -7 5k = 0 + -7 Combine like terms: 0 + -7 = -7 5k = -7 Divide each side by '5'. k = -1.4 Simplifying k = -1.4Subproblem 2
Set the factor '(1 + k)' equal to zero and attempt to solve: Simplifying 1 + k = 0 Solving 1 + k = 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 + k = 0 + -1 Combine like terms: 1 + -1 = 0 0 + k = 0 + -1 k = 0 + -1 Combine like terms: 0 + -1 = -1 k = -1 Simplifying k = -1Solution
k = {-1.4, -1}
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