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Simplifying 4k2 = 15 + -11k Solving 4k2 = 15 + -11k Solving for variable 'k'. Reorder the terms: -15 + 11k + 4k2 = 15 + -11k + -15 + 11k Reorder the terms: -15 + 11k + 4k2 = 15 + -15 + -11k + 11k Combine like terms: 15 + -15 = 0 -15 + 11k + 4k2 = 0 + -11k + 11k -15 + 11k + 4k2 = -11k + 11k Combine like terms: -11k + 11k = 0 -15 + 11k + 4k2 = 0 Factor a trinomial. (-15 + -4k)(1 + -1k) = 0Subproblem 1
Set the factor '(-15 + -4k)' equal to zero and attempt to solve: Simplifying -15 + -4k = 0 Solving -15 + -4k = 0 Move all terms containing k to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + -4k = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -4k = 0 + 15 -4k = 0 + 15 Combine like terms: 0 + 15 = 15 -4k = 15 Divide each side by '-4'. k = -3.75 Simplifying k = -3.75Subproblem 2
Set the factor '(1 + -1k)' equal to zero and attempt to solve: Simplifying 1 + -1k = 0 Solving 1 + -1k = 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 + -1k = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1k = 0 + -1 -1k = 0 + -1 Combine like terms: 0 + -1 = -1 -1k = -1 Divide each side by '-1'. k = 1 Simplifying k = 1Solution
k = {-3.75, 1}
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