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Simplifying 10k(k + 2) = 7k + -4 Reorder the terms: 10k(2 + k) = 7k + -4 (2 * 10k + k * 10k) = 7k + -4 (20k + 10k2) = 7k + -4 Reorder the terms: 20k + 10k2 = -4 + 7k Solving 20k + 10k2 = -4 + 7k Solving for variable 'k'. Reorder the terms: 4 + 20k + -7k + 10k2 = -4 + 7k + 4 + -7k Combine like terms: 20k + -7k = 13k 4 + 13k + 10k2 = -4 + 7k + 4 + -7k Reorder the terms: 4 + 13k + 10k2 = -4 + 4 + 7k + -7k Combine like terms: -4 + 4 = 0 4 + 13k + 10k2 = 0 + 7k + -7k 4 + 13k + 10k2 = 7k + -7k Combine like terms: 7k + -7k = 0 4 + 13k + 10k2 = 0 Factor a trinomial. (4 + 5k)(1 + 2k) = 0Subproblem 1
Set the factor '(4 + 5k)' equal to zero and attempt to solve: Simplifying 4 + 5k = 0 Solving 4 + 5k = 0 Move all terms containing k to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 5k = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 5k = 0 + -4 5k = 0 + -4 Combine like terms: 0 + -4 = -4 5k = -4 Divide each side by '5'. k = -0.8 Simplifying k = -0.8Subproblem 2
Set the factor '(1 + 2k)' equal to zero and attempt to solve: Simplifying 1 + 2k = 0 Solving 1 + 2k = 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 + 2k = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2k = 0 + -1 2k = 0 + -1 Combine like terms: 0 + -1 = -1 2k = -1 Divide each side by '2'. k = -0.5 Simplifying k = -0.5Solution
k = {-0.8, -0.5}
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