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Simplifying (2k + 5)(k + -5) = 0 Reorder the terms: (5 + 2k)(k + -5) = 0 Reorder the terms: (5 + 2k)(-5 + k) = 0 Multiply (5 + 2k) * (-5 + k) (5(-5 + k) + 2k * (-5 + k)) = 0 ((-5 * 5 + k * 5) + 2k * (-5 + k)) = 0 ((-25 + 5k) + 2k * (-5 + k)) = 0 (-25 + 5k + (-5 * 2k + k * 2k)) = 0 (-25 + 5k + (-10k + 2k2)) = 0 Combine like terms: 5k + -10k = -5k (-25 + -5k + 2k2) = 0 Solving -25 + -5k + 2k2 = 0 Solving for variable 'k'. Factor a trinomial. (-5 + -2k)(5 + -1k) = 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 '(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 = {-2.5, 5}
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