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Simplifying 3k2 = 84 + 9k Solving 3k2 = 84 + 9k Solving for variable 'k'. Reorder the terms: -84 + -9k + 3k2 = 84 + 9k + -84 + -9k Reorder the terms: -84 + -9k + 3k2 = 84 + -84 + 9k + -9k Combine like terms: 84 + -84 = 0 -84 + -9k + 3k2 = 0 + 9k + -9k -84 + -9k + 3k2 = 9k + -9k Combine like terms: 9k + -9k = 0 -84 + -9k + 3k2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-28 + -3k + k2) = 0 Factor a trinomial. 3((-4 + -1k)(7 + -1k)) = 0 Ignore the factor 3.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 '(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 = {-4, 7}
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