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Simplifying (5k + 4)(k + -5) = 0 Reorder the terms: (4 + 5k)(k + -5) = 0 Reorder the terms: (4 + 5k)(-5 + k) = 0 Multiply (4 + 5k) * (-5 + k) (4(-5 + k) + 5k * (-5 + k)) = 0 ((-5 * 4 + k * 4) + 5k * (-5 + k)) = 0 ((-20 + 4k) + 5k * (-5 + k)) = 0 (-20 + 4k + (-5 * 5k + k * 5k)) = 0 (-20 + 4k + (-25k + 5k2)) = 0 Combine like terms: 4k + -25k = -21k (-20 + -21k + 5k2) = 0 Solving -20 + -21k + 5k2 = 0 Solving for variable 'k'. Factor a trinomial. (-4 + -5k)(5 + -1k) = 0Subproblem 1
Set the factor '(-4 + -5k)' equal to zero and attempt to solve: Simplifying -4 + -5k = 0 Solving -4 + -5k = 0 Move all terms containing k to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -5k = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -5k = 0 + 4 -5k = 0 + 4 Combine like terms: 0 + 4 = 4 -5k = 4 Divide each side by '-5'. k = -0.8 Simplifying k = -0.8Subproblem 2
Set the factor '(5 + -1k)' equal to zero and attempt to solve: Simplifying 5 + -1k = 0 Solving 5 + -1k = 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 + -1k = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1k = 0 + -5 -1k = 0 + -5 Combine like terms: 0 + -5 = -5 -1k = -5 Divide each side by '-1'. k = 5 Simplifying k = 5Solution
k = {-0.8, 5}
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