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Simplifying k2 = 5k2 + -32k + 48 Reorder the terms: k2 = 48 + -32k + 5k2 Solving k2 = 48 + -32k + 5k2 Solving for variable 'k'. Reorder the terms: -48 + 32k + k2 + -5k2 = 48 + -32k + 5k2 + -48 + 32k + -5k2 Combine like terms: k2 + -5k2 = -4k2 -48 + 32k + -4k2 = 48 + -32k + 5k2 + -48 + 32k + -5k2 Reorder the terms: -48 + 32k + -4k2 = 48 + -48 + -32k + 32k + 5k2 + -5k2 Combine like terms: 48 + -48 = 0 -48 + 32k + -4k2 = 0 + -32k + 32k + 5k2 + -5k2 -48 + 32k + -4k2 = -32k + 32k + 5k2 + -5k2 Combine like terms: -32k + 32k = 0 -48 + 32k + -4k2 = 0 + 5k2 + -5k2 -48 + 32k + -4k2 = 5k2 + -5k2 Combine like terms: 5k2 + -5k2 = 0 -48 + 32k + -4k2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-12 + 8k + -1k2) = 0 Factor a trinomial. 4((-6 + k)(2 + -1k)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-6 + k)' equal to zero and attempt to solve: Simplifying -6 + k = 0 Solving -6 + k = 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 + k = 0 + 6 Combine like terms: -6 + 6 = 0 0 + k = 0 + 6 k = 0 + 6 Combine like terms: 0 + 6 = 6 k = 6 Simplifying k = 6Subproblem 2
Set the factor '(2 + -1k)' equal to zero and attempt to solve: Simplifying 2 + -1k = 0 Solving 2 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1k = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1k = 0 + -2 -1k = 0 + -2 Combine like terms: 0 + -2 = -2 -1k = -2 Divide each side by '-1'. k = 2 Simplifying k = 2Solution
k = {6, 2}
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