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Simplifying 6k2 = 125 + 5k Solving 6k2 = 125 + 5k Solving for variable 'k'. Reorder the terms: -125 + -5k + 6k2 = 125 + 5k + -125 + -5k Reorder the terms: -125 + -5k + 6k2 = 125 + -125 + 5k + -5k Combine like terms: 125 + -125 = 0 -125 + -5k + 6k2 = 0 + 5k + -5k -125 + -5k + 6k2 = 5k + -5k Combine like terms: 5k + -5k = 0 -125 + -5k + 6k2 = 0 Factor a trinomial. (-25 + -6k)(5 + -1k) = 0Subproblem 1
Set the factor '(-25 + -6k)' equal to zero and attempt to solve: Simplifying -25 + -6k = 0 Solving -25 + -6k = 0 Move all terms containing k to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + -6k = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -6k = 0 + 25 -6k = 0 + 25 Combine like terms: 0 + 25 = 25 -6k = 25 Divide each side by '-6'. k = -4.166666667 Simplifying k = -4.166666667Subproblem 2
Set the factor '(5 + -1k)' equal to zero and attempt to solve: Simplifying 5 + -1k = 0 Solving 5 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1k = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1k = 0 + -5 -1k = 0 + -5 Combine like terms: 0 + -5 = -5 -1k = -5 Divide each side by '-1'. k = 5 Simplifying k = 5Solution
k = {-4.166666667, 5}
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