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Simplifying 5(10k + 1) + 2(2 + 8) = 0 Reorder the terms: 5(1 + 10k) + 2(2 + 8) = 0 (1 * 5 + 10k * 5) + 2(2 + 8) = 0 (5 + 50k) + 2(2 + 8) = 0 Combine like terms: 2 + 8 = 10 5 + 50k + 2(10) = 0 Multiply 2 * 10 5 + 50k + 20 = 0 Reorder the terms: 5 + 20 + 50k = 0 Combine like terms: 5 + 20 = 25 25 + 50k = 0 Solving 25 + 50k = 0 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + 50k = 0 + -25 Combine like terms: 25 + -25 = 0 0 + 50k = 0 + -25 50k = 0 + -25 Combine like terms: 0 + -25 = -25 50k = -25 Divide each side by '50'. k = -0.5 Simplifying k = -0.5
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