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Simplifying (5k2 + 8K + 3) + -1(2k + 4) = 0 Reorder the terms: (3 + 8K + 5k2) + -1(2k + 4) = 0 Remove parenthesis around (3 + 8K + 5k2) 3 + 8K + 5k2 + -1(2k + 4) = 0 Reorder the terms: 3 + 8K + 5k2 + -1(4 + 2k) = 0 3 + 8K + 5k2 + (4 * -1 + 2k * -1) = 0 3 + 8K + 5k2 + (-4 + -2k) = 0 Reorder the terms: 3 + -4 + 8K + -2k + 5k2 = 0 Combine like terms: 3 + -4 = -1 -1 + 8K + -2k + 5k2 = 0 Solving -1 + 8K + -2k + 5k2 = 0 Solving for variable 'K'. Move all terms containing K to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 8K + -2k + 1 + 5k2 = 0 + 1 Reorder the terms: -1 + 1 + 8K + -2k + 5k2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 8K + -2k + 5k2 = 0 + 1 8K + -2k + 5k2 = 0 + 1 Combine like terms: 0 + 1 = 1 8K + -2k + 5k2 = 1 Add '2k' to each side of the equation. 8K + -2k + 2k + 5k2 = 1 + 2k Combine like terms: -2k + 2k = 0 8K + 0 + 5k2 = 1 + 2k 8K + 5k2 = 1 + 2k Add '-5k2' to each side of the equation. 8K + 5k2 + -5k2 = 1 + 2k + -5k2 Combine like terms: 5k2 + -5k2 = 0 8K + 0 = 1 + 2k + -5k2 8K = 1 + 2k + -5k2 Divide each side by '8'. K = 0.125 + 0.25k + -0.625k2 Simplifying K = 0.125 + 0.25k + -0.625k2
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