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Simplifying 4k2 = 4 + -15k Solving 4k2 = 4 + -15k Solving for variable 'k'. Reorder the terms: -4 + 15k + 4k2 = 4 + -15k + -4 + 15k Reorder the terms: -4 + 15k + 4k2 = 4 + -4 + -15k + 15k Combine like terms: 4 + -4 = 0 -4 + 15k + 4k2 = 0 + -15k + 15k -4 + 15k + 4k2 = -15k + 15k Combine like terms: -15k + 15k = 0 -4 + 15k + 4k2 = 0 Factor a trinomial. (-4 + -1k)(1 + -4k) = 0Subproblem 1
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 = -4Subproblem 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 = {-4, 0.25}
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