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Simplifying 9k = 10 + -1k2 Solving 9k = 10 + -1k2 Solving for variable 'k'. Reorder the terms: -10 + 9k + k2 = 10 + -1k2 + -10 + k2 Reorder the terms: -10 + 9k + k2 = 10 + -10 + -1k2 + k2 Combine like terms: 10 + -10 = 0 -10 + 9k + k2 = 0 + -1k2 + k2 -10 + 9k + k2 = -1k2 + k2 Combine like terms: -1k2 + k2 = 0 -10 + 9k + k2 = 0 Factor a trinomial. (-10 + -1k)(1 + -1k) = 0Subproblem 1
Set the factor '(-10 + -1k)' equal to zero and attempt to solve: Simplifying -10 + -1k = 0 Solving -10 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + -1k = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -1k = 0 + 10 -1k = 0 + 10 Combine like terms: 0 + 10 = 10 -1k = 10 Divide each side by '-1'. k = -10 Simplifying k = -10Subproblem 2
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 = 1Solution
k = {-10, 1}
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