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Simplifying (7k + 1)(7k + 1) = 0 Reorder the terms: (1 + 7k)(7k + 1) = 0 Reorder the terms: (1 + 7k)(1 + 7k) = 0 Multiply (1 + 7k) * (1 + 7k) (1(1 + 7k) + 7k * (1 + 7k)) = 0 ((1 * 1 + 7k * 1) + 7k * (1 + 7k)) = 0 ((1 + 7k) + 7k * (1 + 7k)) = 0 (1 + 7k + (1 * 7k + 7k * 7k)) = 0 (1 + 7k + (7k + 49k2)) = 0 Combine like terms: 7k + 7k = 14k (1 + 14k + 49k2) = 0 Solving 1 + 14k + 49k2 = 0 Solving for variable 'k'. Factor a trinomial. (1 + 7k)(1 + 7k) = 0Subproblem 1
Set the factor '(1 + 7k)' equal to zero and attempt to solve: Simplifying 1 + 7k = 0 Solving 1 + 7k = 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 + 7k = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 7k = 0 + -1 7k = 0 + -1 Combine like terms: 0 + -1 = -1 7k = -1 Divide each side by '7'. k = -0.1428571429 Simplifying k = -0.1428571429Subproblem 2
Set the factor '(1 + 7k)' equal to zero and attempt to solve: Simplifying 1 + 7k = 0 Solving 1 + 7k = 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 + 7k = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 7k = 0 + -1 7k = 0 + -1 Combine like terms: 0 + -1 = -1 7k = -1 Divide each side by '7'. k = -0.1428571429 Simplifying k = -0.1428571429Solution
k = {-0.1428571429, -0.1428571429}
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