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Simplifying 2k2 + 21k + 8 = -7 + 8k Reorder the terms: 8 + 21k + 2k2 = -7 + 8k Solving 8 + 21k + 2k2 = -7 + 8k Solving for variable 'k'. Reorder the terms: 8 + 7 + 21k + -8k + 2k2 = -7 + 8k + 7 + -8k Combine like terms: 8 + 7 = 15 15 + 21k + -8k + 2k2 = -7 + 8k + 7 + -8k Combine like terms: 21k + -8k = 13k 15 + 13k + 2k2 = -7 + 8k + 7 + -8k Reorder the terms: 15 + 13k + 2k2 = -7 + 7 + 8k + -8k Combine like terms: -7 + 7 = 0 15 + 13k + 2k2 = 0 + 8k + -8k 15 + 13k + 2k2 = 8k + -8k Combine like terms: 8k + -8k = 0 15 + 13k + 2k2 = 0 Factor a trinomial. (5 + k)(3 + 2k) = 0Subproblem 1
Set the factor '(5 + k)' equal to zero and attempt to solve: Simplifying 5 + k = 0 Solving 5 + k = 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 + k = 0 + -5 Combine like terms: 5 + -5 = 0 0 + k = 0 + -5 k = 0 + -5 Combine like terms: 0 + -5 = -5 k = -5 Simplifying k = -5Subproblem 2
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 = -1.5Solution
k = {-5, -1.5}
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