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Simplifying 6k2 = 7k + 24 Reorder the terms: 6k2 = 24 + 7k Solving 6k2 = 24 + 7k Solving for variable 'k'. Reorder the terms: -24 + -7k + 6k2 = 24 + 7k + -24 + -7k Reorder the terms: -24 + -7k + 6k2 = 24 + -24 + 7k + -7k Combine like terms: 24 + -24 = 0 -24 + -7k + 6k2 = 0 + 7k + -7k -24 + -7k + 6k2 = 7k + -7k Combine like terms: 7k + -7k = 0 -24 + -7k + 6k2 = 0 Factor a trinomial. (-3 + -2k)(8 + -3k) = 0Subproblem 1
Set the factor '(-3 + -2k)' equal to zero and attempt to solve: Simplifying -3 + -2k = 0 Solving -3 + -2k = 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 + -2k = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2k = 0 + 3 -2k = 0 + 3 Combine like terms: 0 + 3 = 3 -2k = 3 Divide each side by '-2'. k = -1.5 Simplifying k = -1.5Subproblem 2
Set the factor '(8 + -3k)' equal to zero and attempt to solve: Simplifying 8 + -3k = 0 Solving 8 + -3k = 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 + -3k = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -3k = 0 + -8 -3k = 0 + -8 Combine like terms: 0 + -8 = -8 -3k = -8 Divide each side by '-3'. k = 2.666666667 Simplifying k = 2.666666667Solution
k = {-1.5, 2.666666667}
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