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Simplifying (x + 2 + i)(x + 2 + -1i) = 0 Reorder the terms: (2 + i + x)(x + 2 + -1i) = 0 Reorder the terms: (2 + i + x)(2 + -1i + x) = 0 Multiply (2 + i + x) * (2 + -1i + x) (2(2 + -1i + x) + i(2 + -1i + x) + x(2 + -1i + x)) = 0 ((2 * 2 + -1i * 2 + x * 2) + i(2 + -1i + x) + x(2 + -1i + x)) = 0 ((4 + -2i + 2x) + i(2 + -1i + x) + x(2 + -1i + x)) = 0 (4 + -2i + 2x + (2 * i + -1i * i + x * i) + x(2 + -1i + x)) = 0 Reorder the terms: (4 + -2i + 2x + (2i + ix + -1i2) + x(2 + -1i + x)) = 0 (4 + -2i + 2x + (2i + ix + -1i2) + x(2 + -1i + x)) = 0 (4 + -2i + 2x + 2i + ix + -1i2 + (2 * x + -1i * x + x * x)) = 0 Reorder the terms: (4 + -2i + 2x + 2i + ix + -1i2 + (-1ix + 2x + x2)) = 0 (4 + -2i + 2x + 2i + ix + -1i2 + (-1ix + 2x + x2)) = 0 Reorder the terms: (4 + -2i + 2i + ix + -1ix + -1i2 + 2x + 2x + x2) = 0 Combine like terms: -2i + 2i = 0 (4 + 0 + ix + -1ix + -1i2 + 2x + 2x + x2) = 0 (4 + ix + -1ix + -1i2 + 2x + 2x + x2) = 0 Combine like terms: ix + -1ix = 0 (4 + 0 + -1i2 + 2x + 2x + x2) = 0 (4 + -1i2 + 2x + 2x + x2) = 0 Combine like terms: 2x + 2x = 4x (4 + -1i2 + 4x + x2) = 0 Solving 4 + -1i2 + 4x + x2 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -1i2 + 4x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + -1i2 + 4x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1i2 + 4x + x2 = 0 + -4 -1i2 + 4x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -1i2 + 4x + x2 = -4 Add '-4x' to each side of the equation. -1i2 + 4x + -4x + x2 = -4 + -4x Combine like terms: 4x + -4x = 0 -1i2 + 0 + x2 = -4 + -4x -1i2 + x2 = -4 + -4x Add '-1x2' to each side of the equation. -1i2 + x2 + -1x2 = -4 + -4x + -1x2 Combine like terms: x2 + -1x2 = 0 -1i2 + 0 = -4 + -4x + -1x2 -1i2 = -4 + -4x + -1x2 Divide each side by '-1'. i2 = 4 + 4x + x2 Simplifying i2 = 4 + 4x + x2 Reorder the terms: -4 + i2 + -4x + -1x2 = 4 + 4x + x2 + -4 + -4x + -1x2 Reorder the terms: -4 + i2 + -4x + -1x2 = 4 + -4 + 4x + -4x + x2 + -1x2 Combine like terms: 4 + -4 = 0 -4 + i2 + -4x + -1x2 = 0 + 4x + -4x + x2 + -1x2 -4 + i2 + -4x + -1x2 = 4x + -4x + x2 + -1x2 Combine like terms: 4x + -4x = 0 -4 + i2 + -4x + -1x2 = 0 + x2 + -1x2 -4 + i2 + -4x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -4 + i2 + -4x + -1x2 = 0 The solution to this equation could not be determined.
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