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Simplifying -5(1 + -5k) + -4(2k + 5) = 0 (1 * -5 + -5k * -5) + -4(2k + 5) = 0 (-5 + 25k) + -4(2k + 5) = 0 Reorder the terms: -5 + 25k + -4(5 + 2k) = 0 -5 + 25k + (5 * -4 + 2k * -4) = 0 -5 + 25k + (-20 + -8k) = 0 Reorder the terms: -5 + -20 + 25k + -8k = 0 Combine like terms: -5 + -20 = -25 -25 + 25k + -8k = 0 Combine like terms: 25k + -8k = 17k -25 + 17k = 0 Solving -25 + 17k = 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 + 17k = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 17k = 0 + 25 17k = 0 + 25 Combine like terms: 0 + 25 = 25 17k = 25 Divide each side by '17'. k = 1.470588235 Simplifying k = 1.470588235
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