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Simplifying 2k2 = 16k + 18 Reorder the terms: 2k2 = 18 + 16k Solving 2k2 = 18 + 16k Solving for variable 'k'. Reorder the terms: -18 + -16k + 2k2 = 18 + 16k + -18 + -16k Reorder the terms: -18 + -16k + 2k2 = 18 + -18 + 16k + -16k Combine like terms: 18 + -18 = 0 -18 + -16k + 2k2 = 0 + 16k + -16k -18 + -16k + 2k2 = 16k + -16k Combine like terms: 16k + -16k = 0 -18 + -16k + 2k2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-9 + -8k + k2) = 0 Factor a trinomial. 2((-1 + -1k)(9 + -1k)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + -1k)' equal to zero and attempt to solve: Simplifying -1 + -1k = 0 Solving -1 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1k = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1k = 0 + 1 -1k = 0 + 1 Combine like terms: 0 + 1 = 1 -1k = 1 Divide each side by '-1'. k = -1 Simplifying k = -1Subproblem 2
Set the factor '(9 + -1k)' equal to zero and attempt to solve: Simplifying 9 + -1k = 0 Solving 9 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1k = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1k = 0 + -9 -1k = 0 + -9 Combine like terms: 0 + -9 = -9 -1k = -9 Divide each side by '-1'. k = 9 Simplifying k = 9Solution
k = {-1, 9}
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