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Simplifying 9k2 + 6k + -22 = 8k2 + k + -8 Reorder the terms: -22 + 6k + 9k2 = 8k2 + k + -8 Reorder the terms: -22 + 6k + 9k2 = -8 + k + 8k2 Solving -22 + 6k + 9k2 = -8 + k + 8k2 Solving for variable 'k'. Reorder the terms: -22 + 8 + 6k + -1k + 9k2 + -8k2 = -8 + k + 8k2 + 8 + -1k + -8k2 Combine like terms: -22 + 8 = -14 -14 + 6k + -1k + 9k2 + -8k2 = -8 + k + 8k2 + 8 + -1k + -8k2 Combine like terms: 6k + -1k = 5k -14 + 5k + 9k2 + -8k2 = -8 + k + 8k2 + 8 + -1k + -8k2 Combine like terms: 9k2 + -8k2 = 1k2 -14 + 5k + 1k2 = -8 + k + 8k2 + 8 + -1k + -8k2 Reorder the terms: -14 + 5k + 1k2 = -8 + 8 + k + -1k + 8k2 + -8k2 Combine like terms: -8 + 8 = 0 -14 + 5k + 1k2 = 0 + k + -1k + 8k2 + -8k2 -14 + 5k + 1k2 = k + -1k + 8k2 + -8k2 Combine like terms: k + -1k = 0 -14 + 5k + 1k2 = 0 + 8k2 + -8k2 -14 + 5k + 1k2 = 8k2 + -8k2 Combine like terms: 8k2 + -8k2 = 0 -14 + 5k + 1k2 = 0 Factor a trinomial. (-7 + -1k)(2 + -1k) = 0Subproblem 1
Set the factor '(-7 + -1k)' equal to zero and attempt to solve: Simplifying -7 + -1k = 0 Solving -7 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -1k = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1k = 0 + 7 -1k = 0 + 7 Combine like terms: 0 + 7 = 7 -1k = 7 Divide each side by '-1'. k = -7 Simplifying k = -7Subproblem 2
Set the factor '(2 + -1k)' equal to zero and attempt to solve: Simplifying 2 + -1k = 0 Solving 2 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1k = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1k = 0 + -2 -1k = 0 + -2 Combine like terms: 0 + -2 = -2 -1k = -2 Divide each side by '-1'. k = 2 Simplifying k = 2Solution
k = {-7, 2}
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