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Simplifying -5(1 + 5k) * 4 + -1(2k + 5) = 0 Reorder the terms for easier multiplication: -5 * 4(1 + 5k) + -1(2k + 5) = 0 Multiply -5 * 4 -20(1 + 5k) + -1(2k + 5) = 0 (1 * -20 + 5k * -20) + -1(2k + 5) = 0 (-20 + -100k) + -1(2k + 5) = 0 Reorder the terms: -20 + -100k + -1(5 + 2k) = 0 -20 + -100k + (5 * -1 + 2k * -1) = 0 -20 + -100k + (-5 + -2k) = 0 Reorder the terms: -20 + -5 + -100k + -2k = 0 Combine like terms: -20 + -5 = -25 -25 + -100k + -2k = 0 Combine like terms: -100k + -2k = -102k -25 + -102k = 0 Solving -25 + -102k = 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 + -102k = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -102k = 0 + 25 -102k = 0 + 25 Combine like terms: 0 + 25 = 25 -102k = 25 Divide each side by '-102'. k = -0.2450980392 Simplifying k = -0.2450980392
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