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Simplifying (7k + 2)(k + 7) = 0 Reorder the terms: (2 + 7k)(k + 7) = 0 Reorder the terms: (2 + 7k)(7 + k) = 0 Multiply (2 + 7k) * (7 + k) (2(7 + k) + 7k * (7 + k)) = 0 ((7 * 2 + k * 2) + 7k * (7 + k)) = 0 ((14 + 2k) + 7k * (7 + k)) = 0 (14 + 2k + (7 * 7k + k * 7k)) = 0 (14 + 2k + (49k + 7k2)) = 0 Combine like terms: 2k + 49k = 51k (14 + 51k + 7k2) = 0 Solving 14 + 51k + 7k2 = 0 Solving for variable 'k'. Factor a trinomial. (7 + k)(2 + 7k) = 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 '(2 + 7k)' equal to zero and attempt to solve: Simplifying 2 + 7k = 0 Solving 2 + 7k = 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 + 7k = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 7k = 0 + -2 7k = 0 + -2 Combine like terms: 0 + -2 = -2 7k = -2 Divide each side by '7'. k = -0.2857142857 Simplifying k = -0.2857142857Solution
k = {-7, -0.2857142857}
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