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