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Simplifying x2 + (2k + -1) * x + 1 = 0 Reorder the terms: x2 + (-1 + 2k) * x + 1 = 0 Reorder the terms for easier multiplication: x2 + x(-1 + 2k) + 1 = 0 x2 + (-1 * x + 2k * x) + 1 = 0 Reorder the terms: x2 + (2kx + -1x) + 1 = 0 x2 + (2kx + -1x) + 1 = 0 Reorder the terms: 1 + 2kx + -1x + x2 = 0 Solving 1 + 2kx + -1x + x2 = 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 + 2kx + -1x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 2kx + -1x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2kx + -1x + x2 = 0 + -1 2kx + -1x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 2kx + -1x + x2 = -1 Add 'x' to each side of the equation. 2kx + -1x + x + x2 = -1 + x Combine like terms: -1x + x = 0 2kx + 0 + x2 = -1 + x 2kx + x2 = -1 + x Add '-1x2' to each side of the equation. 2kx + x2 + -1x2 = -1 + x + -1x2 Combine like terms: x2 + -1x2 = 0 2kx + 0 = -1 + x + -1x2 2kx = -1 + x + -1x2 Divide each side by '2x'. k = -0.5x-1 + 0.5 + -0.5x Simplifying k = -0.5x-1 + 0.5 + -0.5x Reorder the terms: k = 0.5 + -0.5x-1 + -0.5x
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