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Simplifying -5k2 + 11k + 52 = 4k Reorder the terms: 52 + 11k + -5k2 = 4k Solving 52 + 11k + -5k2 = 4k Solving for variable 'k'. Reorder the terms: 52 + 11k + -4k + -5k2 = 4k + -4k Combine like terms: 11k + -4k = 7k 52 + 7k + -5k2 = 4k + -4k Combine like terms: 4k + -4k = 0 52 + 7k + -5k2 = 0 Factor a trinomial. (4 + -1k)(13 + 5k) = 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 '(13 + 5k)' equal to zero and attempt to solve: Simplifying 13 + 5k = 0 Solving 13 + 5k = 0 Move all terms containing k to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + 5k = 0 + -13 Combine like terms: 13 + -13 = 0 0 + 5k = 0 + -13 5k = 0 + -13 Combine like terms: 0 + -13 = -13 5k = -13 Divide each side by '5'. k = -2.6 Simplifying k = -2.6Solution
k = {4, -2.6}
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