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Simplifying 12 + -3k = 2k2 + 7 Reorder the terms: 12 + -3k = 7 + 2k2 Solving 12 + -3k = 7 + 2k2 Solving for variable 'k'. Reorder the terms: 12 + -7 + -3k + -2k2 = 7 + 2k2 + -7 + -2k2 Combine like terms: 12 + -7 = 5 5 + -3k + -2k2 = 7 + 2k2 + -7 + -2k2 Reorder the terms: 5 + -3k + -2k2 = 7 + -7 + 2k2 + -2k2 Combine like terms: 7 + -7 = 0 5 + -3k + -2k2 = 0 + 2k2 + -2k2 5 + -3k + -2k2 = 2k2 + -2k2 Combine like terms: 2k2 + -2k2 = 0 5 + -3k + -2k2 = 0 Factor a trinomial. (1 + -1k)(5 + 2k) = 0Subproblem 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 '(5 + 2k)' equal to zero and attempt to solve: Simplifying 5 + 2k = 0 Solving 5 + 2k = 0 Move all terms containing k to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 2k = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2k = 0 + -5 2k = 0 + -5 Combine like terms: 0 + -5 = -5 2k = -5 Divide each side by '2'. k = -2.5 Simplifying k = -2.5Solution
k = {1, -2.5}
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