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Simplifying 2x2 + -3x + -1(k + 1) = 0 Reorder the terms: 2x2 + -3x + -1(1 + k) = 0 2x2 + -3x + (1 * -1 + k * -1) = 0 2x2 + -3x + (-1 + -1k) = 0 Reorder the terms: -1 + -1k + -3x + 2x2 = 0 Solving -1 + -1k + -3x + 2x2 = 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 + -1k + -3x + 1 + 2x2 = 0 + 1 Reorder the terms: -1 + 1 + -1k + -3x + 2x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1k + -3x + 2x2 = 0 + 1 -1k + -3x + 2x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -1k + -3x + 2x2 = 1 Add '3x' to each side of the equation. -1k + -3x + 3x + 2x2 = 1 + 3x Combine like terms: -3x + 3x = 0 -1k + 0 + 2x2 = 1 + 3x -1k + 2x2 = 1 + 3x Add '-2x2' to each side of the equation. -1k + 2x2 + -2x2 = 1 + 3x + -2x2 Combine like terms: 2x2 + -2x2 = 0 -1k + 0 = 1 + 3x + -2x2 -1k = 1 + 3x + -2x2 Divide each side by '-1'. k = -1 + -3x + 2x2 Simplifying k = -1 + -3x + 2x2
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