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Simplifying 3k2 + -12k + 12 = 75 Reorder the terms: 12 + -12k + 3k2 = 75 Solving 12 + -12k + 3k2 = 75 Solving for variable 'k'. Reorder the terms: 12 + -75 + -12k + 3k2 = 75 + -75 Combine like terms: 12 + -75 = -63 -63 + -12k + 3k2 = 75 + -75 Combine like terms: 75 + -75 = 0 -63 + -12k + 3k2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-21 + -4k + k2) = 0 Factor a trinomial. 3((-3 + -1k)(7 + -1k)) = 0 Ignore the factor 3.Subproblem 1
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 = -3Subproblem 2
Set the factor '(7 + -1k)' equal to zero and attempt to solve: Simplifying 7 + -1k = 0 Solving 7 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1k = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1k = 0 + -7 -1k = 0 + -7 Combine like terms: 0 + -7 = -7 -1k = -7 Divide each side by '-1'. k = 7 Simplifying k = 7Solution
k = {-3, 7}
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