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Simplifying 5k2 = -24 + 43k Solving 5k2 = -24 + 43k Solving for variable 'k'. Reorder the terms: 24 + -43k + 5k2 = -24 + 43k + 24 + -43k Reorder the terms: 24 + -43k + 5k2 = -24 + 24 + 43k + -43k Combine like terms: -24 + 24 = 0 24 + -43k + 5k2 = 0 + 43k + -43k 24 + -43k + 5k2 = 43k + -43k Combine like terms: 43k + -43k = 0 24 + -43k + 5k2 = 0 Factor a trinomial. (3 + -5k)(8 + -1k) = 0Subproblem 1
Set the factor '(3 + -5k)' equal to zero and attempt to solve: Simplifying 3 + -5k = 0 Solving 3 + -5k = 0 Move all terms containing k to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -5k = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5k = 0 + -3 -5k = 0 + -3 Combine like terms: 0 + -3 = -3 -5k = -3 Divide each side by '-5'. k = 0.6 Simplifying k = 0.6Subproblem 2
Set the factor '(8 + -1k)' equal to zero and attempt to solve: Simplifying 8 + -1k = 0 Solving 8 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1k = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1k = 0 + -8 -1k = 0 + -8 Combine like terms: 0 + -8 = -8 -1k = -8 Divide each side by '-1'. k = 8 Simplifying k = 8Solution
k = {0.6, 8}
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