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Simplifying 15k2 + 33k + -192 = -7k + 7k2 Reorder the terms: -192 + 33k + 15k2 = -7k + 7k2 Solving -192 + 33k + 15k2 = -7k + 7k2 Solving for variable 'k'. Reorder the terms: -192 + 33k + 7k + 15k2 + -7k2 = -7k + 7k2 + 7k + -7k2 Combine like terms: 33k + 7k = 40k -192 + 40k + 15k2 + -7k2 = -7k + 7k2 + 7k + -7k2 Combine like terms: 15k2 + -7k2 = 8k2 -192 + 40k + 8k2 = -7k + 7k2 + 7k + -7k2 Reorder the terms: -192 + 40k + 8k2 = -7k + 7k + 7k2 + -7k2 Combine like terms: -7k + 7k = 0 -192 + 40k + 8k2 = 0 + 7k2 + -7k2 -192 + 40k + 8k2 = 7k2 + -7k2 Combine like terms: 7k2 + -7k2 = 0 -192 + 40k + 8k2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(-24 + 5k + k2) = 0 Factor a trinomial. 8((-8 + -1k)(3 + -1k)) = 0 Ignore the factor 8.Subproblem 1
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 = -8Subproblem 2
Set the factor '(3 + -1k)' equal to zero and attempt to solve: Simplifying 3 + -1k = 0 Solving 3 + -1k = 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 + -1k = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1k = 0 + -3 -1k = 0 + -3 Combine like terms: 0 + -3 = -3 -1k = -3 Divide each side by '-1'. k = 3 Simplifying k = 3Solution
k = {-8, 3}
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