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Simplifying 5(9k + 2) + 8(3 + 4k) = 0 Reorder the terms: 5(2 + 9k) + 8(3 + 4k) = 0 (2 * 5 + 9k * 5) + 8(3 + 4k) = 0 (10 + 45k) + 8(3 + 4k) = 0 10 + 45k + (3 * 8 + 4k * 8) = 0 10 + 45k + (24 + 32k) = 0 Reorder the terms: 10 + 24 + 45k + 32k = 0 Combine like terms: 10 + 24 = 34 34 + 45k + 32k = 0 Combine like terms: 45k + 32k = 77k 34 + 77k = 0 Solving 34 + 77k = 0 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-34' to each side of the equation. 34 + -34 + 77k = 0 + -34 Combine like terms: 34 + -34 = 0 0 + 77k = 0 + -34 77k = 0 + -34 Combine like terms: 0 + -34 = -34 77k = -34 Divide each side by '77'. k = -0.4415584416 Simplifying k = -0.4415584416
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