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Simplifying (4k + -1)(4k + -5) = 0 Reorder the terms: (-1 + 4k)(4k + -5) = 0 Reorder the terms: (-1 + 4k)(-5 + 4k) = 0 Multiply (-1 + 4k) * (-5 + 4k) (-1(-5 + 4k) + 4k * (-5 + 4k)) = 0 ((-5 * -1 + 4k * -1) + 4k * (-5 + 4k)) = 0 ((5 + -4k) + 4k * (-5 + 4k)) = 0 (5 + -4k + (-5 * 4k + 4k * 4k)) = 0 (5 + -4k + (-20k + 16k2)) = 0 Combine like terms: -4k + -20k = -24k (5 + -24k + 16k2) = 0 Solving 5 + -24k + 16k2 = 0 Solving for variable 'k'. Factor a trinomial. (1 + -4k)(5 + -4k) = 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 '(5 + -4k)' equal to zero and attempt to solve: Simplifying 5 + -4k = 0 Solving 5 + -4k = 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 + -4k = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4k = 0 + -5 -4k = 0 + -5 Combine like terms: 0 + -5 = -5 -4k = -5 Divide each side by '-4'. k = 1.25 Simplifying k = 1.25Solution
k = {0.25, 1.25}
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