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Simplifying 2k2 + -14k + -30 = k2 + 3k + 30 Reorder the terms: -30 + -14k + 2k2 = k2 + 3k + 30 Reorder the terms: -30 + -14k + 2k2 = 30 + 3k + k2 Solving -30 + -14k + 2k2 = 30 + 3k + k2 Solving for variable 'k'. Reorder the terms: -30 + -30 + -14k + -3k + 2k2 + -1k2 = 30 + 3k + k2 + -30 + -3k + -1k2 Combine like terms: -30 + -30 = -60 -60 + -14k + -3k + 2k2 + -1k2 = 30 + 3k + k2 + -30 + -3k + -1k2 Combine like terms: -14k + -3k = -17k -60 + -17k + 2k2 + -1k2 = 30 + 3k + k2 + -30 + -3k + -1k2 Combine like terms: 2k2 + -1k2 = 1k2 -60 + -17k + 1k2 = 30 + 3k + k2 + -30 + -3k + -1k2 Reorder the terms: -60 + -17k + 1k2 = 30 + -30 + 3k + -3k + k2 + -1k2 Combine like terms: 30 + -30 = 0 -60 + -17k + 1k2 = 0 + 3k + -3k + k2 + -1k2 -60 + -17k + 1k2 = 3k + -3k + k2 + -1k2 Combine like terms: 3k + -3k = 0 -60 + -17k + 1k2 = 0 + k2 + -1k2 -60 + -17k + 1k2 = k2 + -1k2 Combine like terms: k2 + -1k2 = 0 -60 + -17k + 1k2 = 0 Factor a trinomial. (-3 + -1k)(20 + -1k) = 0Subproblem 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 '(20 + -1k)' equal to zero and attempt to solve: Simplifying 20 + -1k = 0 Solving 20 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + -1k = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -1k = 0 + -20 -1k = 0 + -20 Combine like terms: 0 + -20 = -20 -1k = -20 Divide each side by '-1'. k = 20 Simplifying k = 20Solution
k = {-3, 20}
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