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Simplifying (7k + -2)(8k + -1) = 0 Reorder the terms: (-2 + 7k)(8k + -1) = 0 Reorder the terms: (-2 + 7k)(-1 + 8k) = 0 Multiply (-2 + 7k) * (-1 + 8k) (-2(-1 + 8k) + 7k * (-1 + 8k)) = 0 ((-1 * -2 + 8k * -2) + 7k * (-1 + 8k)) = 0 ((2 + -16k) + 7k * (-1 + 8k)) = 0 (2 + -16k + (-1 * 7k + 8k * 7k)) = 0 (2 + -16k + (-7k + 56k2)) = 0 Combine like terms: -16k + -7k = -23k (2 + -23k + 56k2) = 0 Solving 2 + -23k + 56k2 = 0 Solving for variable 'k'. Factor a trinomial. (1 + -8k)(2 + -7k) = 0Subproblem 1
Set the factor '(1 + -8k)' equal to zero and attempt to solve: Simplifying 1 + -8k = 0 Solving 1 + -8k = 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 + -8k = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -8k = 0 + -1 -8k = 0 + -1 Combine like terms: 0 + -1 = -1 -8k = -1 Divide each side by '-8'. k = 0.125 Simplifying k = 0.125Subproblem 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 = {0.125, 0.2857142857}
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