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Simplifying (5k + -2)(9k + 20) = 0 Reorder the terms: (-2 + 5k)(9k + 20) = 0 Reorder the terms: (-2 + 5k)(20 + 9k) = 0 Multiply (-2 + 5k) * (20 + 9k) (-2(20 + 9k) + 5k * (20 + 9k)) = 0 ((20 * -2 + 9k * -2) + 5k * (20 + 9k)) = 0 ((-40 + -18k) + 5k * (20 + 9k)) = 0 (-40 + -18k + (20 * 5k + 9k * 5k)) = 0 (-40 + -18k + (100k + 45k2)) = 0 Combine like terms: -18k + 100k = 82k (-40 + 82k + 45k2) = 0 Solving -40 + 82k + 45k2 = 0 Solving for variable 'k'. Factor a trinomial. (-20 + -9k)(2 + -5k) = 0Subproblem 1
Set the factor '(-20 + -9k)' equal to zero and attempt to solve: Simplifying -20 + -9k = 0 Solving -20 + -9k = 0 Move all terms containing k to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + -9k = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -9k = 0 + 20 -9k = 0 + 20 Combine like terms: 0 + 20 = 20 -9k = 20 Divide each side by '-9'. k = -2.222222222 Simplifying k = -2.222222222Subproblem 2
Set the factor '(2 + -5k)' equal to zero and attempt to solve: Simplifying 2 + -5k = 0 Solving 2 + -5k = 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 + -5k = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5k = 0 + -2 -5k = 0 + -2 Combine like terms: 0 + -2 = -2 -5k = -2 Divide each side by '-5'. k = 0.4 Simplifying k = 0.4Solution
k = {-2.222222222, 0.4}
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