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Simplifying 10 + -22k = -10k2 + 7k Reorder the terms: 10 + -22k = 7k + -10k2 Solving 10 + -22k = 7k + -10k2 Solving for variable 'k'. Combine like terms: -22k + -7k = -29k 10 + -29k + 10k2 = 7k + -10k2 + -7k + 10k2 Reorder the terms: 10 + -29k + 10k2 = 7k + -7k + -10k2 + 10k2 Combine like terms: 7k + -7k = 0 10 + -29k + 10k2 = 0 + -10k2 + 10k2 10 + -29k + 10k2 = -10k2 + 10k2 Combine like terms: -10k2 + 10k2 = 0 10 + -29k + 10k2 = 0 Factor a trinomial. (2 + -5k)(5 + -2k) = 0Subproblem 1
Set the factor '(2 + -5k)' equal to zero and attempt to solve: Simplifying 2 + -5k = 0 Solving 2 + -5k = 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 + -5k = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5k = 0 + -2 -5k = 0 + -2 Combine like terms: 0 + -2 = -2 -5k = -2 Divide each side by '-5'. k = 0.4 Simplifying k = 0.4Subproblem 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 = {0.4, 2.5}
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