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Simplifying 2k2 = 9 + 3k Solving 2k2 = 9 + 3k Solving for variable 'k'. Reorder the terms: -9 + -3k + 2k2 = 9 + 3k + -9 + -3k Reorder the terms: -9 + -3k + 2k2 = 9 + -9 + 3k + -3k Combine like terms: 9 + -9 = 0 -9 + -3k + 2k2 = 0 + 3k + -3k -9 + -3k + 2k2 = 3k + -3k Combine like terms: 3k + -3k = 0 -9 + -3k + 2k2 = 0 Factor a trinomial. (-3 + -2k)(3 + -1k) = 0Subproblem 1
Set the factor '(-3 + -2k)' equal to zero and attempt to solve: Simplifying -3 + -2k = 0 Solving -3 + -2k = 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 + -2k = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2k = 0 + 3 -2k = 0 + 3 Combine like terms: 0 + 3 = 3 -2k = 3 Divide each side by '-2'. k = -1.5 Simplifying k = -1.5Subproblem 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 = {-1.5, 3}
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