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Simplifying (4k + -1)(k + 2) = 0 Reorder the terms: (-1 + 4k)(k + 2) = 0 Reorder the terms: (-1 + 4k)(2 + k) = 0 Multiply (-1 + 4k) * (2 + k) (-1(2 + k) + 4k * (2 + k)) = 0 ((2 * -1 + k * -1) + 4k * (2 + k)) = 0 ((-2 + -1k) + 4k * (2 + k)) = 0 (-2 + -1k + (2 * 4k + k * 4k)) = 0 (-2 + -1k + (8k + 4k2)) = 0 Combine like terms: -1k + 8k = 7k (-2 + 7k + 4k2) = 0 Solving -2 + 7k + 4k2 = 0 Solving for variable 'k'. Factor a trinomial. (-2 + -1k)(1 + -4k) = 0Subproblem 1
Set the factor '(-2 + -1k)' equal to zero and attempt to solve: Simplifying -2 + -1k = 0 Solving -2 + -1k = 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 + -1k = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1k = 0 + 2 -1k = 0 + 2 Combine like terms: 0 + 2 = 2 -1k = 2 Divide each side by '-1'. k = -2 Simplifying k = -2Subproblem 2
Set the factor '(1 + -4k)' equal to zero and attempt to solve: Simplifying 1 + -4k = 0 Solving 1 + -4k = 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 + -4k = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4k = 0 + -1 -4k = 0 + -1 Combine like terms: 0 + -1 = -1 -4k = -1 Divide each side by '-4'. k = 0.25 Simplifying k = 0.25Solution
k = {-2, 0.25}
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