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Simplifying (8k + -1)(9k + -5) = 0 Reorder the terms: (-1 + 8k)(9k + -5) = 0 Reorder the terms: (-1 + 8k)(-5 + 9k) = 0 Multiply (-1 + 8k) * (-5 + 9k) (-1(-5 + 9k) + 8k * (-5 + 9k)) = 0 ((-5 * -1 + 9k * -1) + 8k * (-5 + 9k)) = 0 ((5 + -9k) + 8k * (-5 + 9k)) = 0 (5 + -9k + (-5 * 8k + 9k * 8k)) = 0 (5 + -9k + (-40k + 72k2)) = 0 Combine like terms: -9k + -40k = -49k (5 + -49k + 72k2) = 0 Solving 5 + -49k + 72k2 = 0 Solving for variable 'k'. Factor a trinomial. (1 + -8k)(5 + -9k) = 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 '(5 + -9k)' equal to zero and attempt to solve: Simplifying 5 + -9k = 0 Solving 5 + -9k = 0 Move all terms containing k to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -9k = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -9k = 0 + -5 -9k = 0 + -5 Combine like terms: 0 + -5 = -5 -9k = -5 Divide each side by '-9'. k = 0.5555555556 Simplifying k = 0.5555555556Solution
k = {0.125, 0.5555555556}
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