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Simplifying x2 + 5x + -1(2k + 4) = 0 Reorder the terms: x2 + 5x + -1(4 + 2k) = 0 x2 + 5x + (4 * -1 + 2k * -1) = 0 x2 + 5x + (-4 + -2k) = 0 Reorder the terms: -4 + -2k + 5x + x2 = 0 Solving -4 + -2k + 5x + x2 = 0 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '4' to each side of the equation. -4 + -2k + 5x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -2k + 5x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -2k + 5x + x2 = 0 + 4 -2k + 5x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -2k + 5x + x2 = 4 Add '-5x' to each side of the equation. -2k + 5x + -5x + x2 = 4 + -5x Combine like terms: 5x + -5x = 0 -2k + 0 + x2 = 4 + -5x -2k + x2 = 4 + -5x Add '-1x2' to each side of the equation. -2k + x2 + -1x2 = 4 + -5x + -1x2 Combine like terms: x2 + -1x2 = 0 -2k + 0 = 4 + -5x + -1x2 -2k = 4 + -5x + -1x2 Divide each side by '-2'. k = -2 + 2.5x + 0.5x2 Simplifying k = -2 + 2.5x + 0.5x2
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