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