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Simplifying 4k2 + 4k + -36 = 12 Reorder the terms: -36 + 4k + 4k2 = 12 Solving -36 + 4k + 4k2 = 12 Solving for variable 'k'. Reorder the terms: -36 + -12 + 4k + 4k2 = 12 + -12 Combine like terms: -36 + -12 = -48 -48 + 4k + 4k2 = 12 + -12 Combine like terms: 12 + -12 = 0 -48 + 4k + 4k2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-12 + k + k2) = 0 Factor a trinomial. 4((-4 + -1k)(3 + -1k)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-4 + -1k)' equal to zero and attempt to solve: Simplifying -4 + -1k = 0 Solving -4 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1k = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1k = 0 + 4 -1k = 0 + 4 Combine like terms: 0 + 4 = 4 -1k = 4 Divide each side by '-1'. k = -4 Simplifying k = -4Subproblem 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 = {-4, 3}
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