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Simplifying (4k + -1)(k + -4) = 0 Reorder the terms: (-1 + 4k)(k + -4) = 0 Reorder the terms: (-1 + 4k)(-4 + k) = 0 Multiply (-1 + 4k) * (-4 + k) (-1(-4 + k) + 4k * (-4 + k)) = 0 ((-4 * -1 + k * -1) + 4k * (-4 + k)) = 0 ((4 + -1k) + 4k * (-4 + k)) = 0 (4 + -1k + (-4 * 4k + k * 4k)) = 0 (4 + -1k + (-16k + 4k2)) = 0 Combine like terms: -1k + -16k = -17k (4 + -17k + 4k2) = 0 Solving 4 + -17k + 4k2 = 0 Solving for variable 'k'. Factor a trinomial. (1 + -4k)(4 + -1k) = 0Subproblem 1
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 = 0.25Subproblem 2
Set the factor '(4 + -1k)' equal to zero and attempt to solve: Simplifying 4 + -1k = 0 Solving 4 + -1k = 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 + -1k = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1k = 0 + -4 -1k = 0 + -4 Combine like terms: 0 + -4 = -4 -1k = -4 Divide each side by '-1'. k = 4 Simplifying k = 4Solution
k = {0.25, 4}
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