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Simplifying (5k + -8)(2k + 5) = 0 Reorder the terms: (-8 + 5k)(2k + 5) = 0 Reorder the terms: (-8 + 5k)(5 + 2k) = 0 Multiply (-8 + 5k) * (5 + 2k) (-8(5 + 2k) + 5k * (5 + 2k)) = 0 ((5 * -8 + 2k * -8) + 5k * (5 + 2k)) = 0 ((-40 + -16k) + 5k * (5 + 2k)) = 0 (-40 + -16k + (5 * 5k + 2k * 5k)) = 0 (-40 + -16k + (25k + 10k2)) = 0 Combine like terms: -16k + 25k = 9k (-40 + 9k + 10k2) = 0 Solving -40 + 9k + 10k2 = 0 Solving for variable 'k'. Factor a trinomial. (-5 + -2k)(8 + -5k) = 0Subproblem 1
Set the factor '(-5 + -2k)' equal to zero and attempt to solve: Simplifying -5 + -2k = 0 Solving -5 + -2k = 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 + -2k = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2k = 0 + 5 -2k = 0 + 5 Combine like terms: 0 + 5 = 5 -2k = 5 Divide each side by '-2'. k = -2.5 Simplifying k = -2.5Subproblem 2
Set the factor '(8 + -5k)' equal to zero and attempt to solve: Simplifying 8 + -5k = 0 Solving 8 + -5k = 0 Move all terms containing k to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -5k = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -5k = 0 + -8 -5k = 0 + -8 Combine like terms: 0 + -8 = -8 -5k = -8 Divide each side by '-5'. k = 1.6 Simplifying k = 1.6Solution
k = {-2.5, 1.6}
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