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Simplifying k2 + 3k = 24 + 5k Reorder the terms: 3k + k2 = 24 + 5k Solving 3k + k2 = 24 + 5k Solving for variable 'k'. Reorder the terms: -24 + 3k + -5k + k2 = 24 + 5k + -24 + -5k Combine like terms: 3k + -5k = -2k -24 + -2k + k2 = 24 + 5k + -24 + -5k Reorder the terms: -24 + -2k + k2 = 24 + -24 + 5k + -5k Combine like terms: 24 + -24 = 0 -24 + -2k + k2 = 0 + 5k + -5k -24 + -2k + k2 = 5k + -5k Combine like terms: 5k + -5k = 0 -24 + -2k + k2 = 0 Factor a trinomial. (-4 + -1k)(6 + -1k) = 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 '(6 + -1k)' equal to zero and attempt to solve: Simplifying 6 + -1k = 0 Solving 6 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1k = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1k = 0 + -6 -1k = 0 + -6 Combine like terms: 0 + -6 = -6 -1k = -6 Divide each side by '-1'. k = 6 Simplifying k = 6Solution
k = {-4, 6}
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