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Simplifying (x + 2)(x + (1 + i))(x + (1 + -1i)) = 0 Reorder the terms: (2 + x)(x + (1 + i))(x + (1 + -1i)) = 0 Remove parenthesis around (1 + i) (2 + x)(x + 1 + i)(x + (1 + -1i)) = 0 Reorder the terms: (2 + x)(1 + i + x)(x + (1 + -1i)) = 0 Remove parenthesis around (1 + -1i) (2 + x)(1 + i + x)(x + 1 + -1i) = 0 Reorder the terms: (2 + x)(1 + i + x)(1 + -1i + x) = 0 Multiply (2 + x) * (1 + i + x) (2(1 + i + x) + x(1 + i + x))(1 + -1i + x) = 0 ((1 * 2 + i * 2 + x * 2) + x(1 + i + x))(1 + -1i + x) = 0 ((2 + 2i + 2x) + x(1 + i + x))(1 + -1i + x) = 0 (2 + 2i + 2x + (1 * x + i * x + x * x))(1 + -1i + x) = 0 Reorder the terms: (2 + 2i + 2x + (ix + 1x + x2))(1 + -1i + x) = 0 (2 + 2i + 2x + (ix + 1x + x2))(1 + -1i + x) = 0 Reorder the terms: (2 + 2i + ix + 2x + 1x + x2)(1 + -1i + x) = 0 Combine like terms: 2x + 1x = 3x (2 + 2i + ix + 3x + x2)(1 + -1i + x) = 0 Multiply (2 + 2i + ix + 3x + x2) * (1 + -1i + x) (2(1 + -1i + x) + 2i * (1 + -1i + x) + ix(1 + -1i + x) + 3x * (1 + -1i + x) + x2(1 + -1i + x)) = 0 ((1 * 2 + -1i * 2 + x * 2) + 2i * (1 + -1i + x) + ix(1 + -1i + x) + 3x * (1 + -1i + x) + x2(1 + -1i + x)) = 0 ((2 + -2i + 2x) + 2i * (1 + -1i + x) + ix(1 + -1i + x) + 3x * (1 + -1i + x) + x2(1 + -1i + x)) = 0 (2 + -2i + 2x + (1 * 2i + -1i * 2i + x * 2i) + ix(1 + -1i + x) + 3x * (1 + -1i + x) + x2(1 + -1i + x)) = 0 Reorder the terms: (2 + -2i + 2x + (2i + 2ix + -2i2) + ix(1 + -1i + x) + 3x * (1 + -1i + x) + x2(1 + -1i + x)) = 0 (2 + -2i + 2x + (2i + 2ix + -2i2) + ix(1 + -1i + x) + 3x * (1 + -1i + x) + x2(1 + -1i + x)) = 0 (2 + -2i + 2x + 2i + 2ix + -2i2 + (1 * ix + -1i * ix + x * ix) + 3x * (1 + -1i + x) + x2(1 + -1i + x)) = 0 Reorder the terms: (2 + -2i + 2x + 2i + 2ix + -2i2 + (1ix + ix2 + -1i2x) + 3x * (1 + -1i + x) + x2(1 + -1i + x)) = 0 (2 + -2i + 2x + 2i + 2ix + -2i2 + (1ix + ix2 + -1i2x) + 3x * (1 + -1i + x) + x2(1 + -1i + x)) = 0 (2 + -2i + 2x + 2i + 2ix + -2i2 + 1ix + ix2 + -1i2x + (1 * 3x + -1i * 3x + x * 3x) + x2(1 + -1i + x)) = 0 Reorder the terms: (2 + -2i + 2x + 2i + 2ix + -2i2 + 1ix + ix2 + -1i2x + (-3ix + 3x + 3x2) + x2(1 + -1i + x)) = 0 (2 + -2i + 2x + 2i + 2ix + -2i2 + 1ix + ix2 + -1i2x + (-3ix + 3x + 3x2) + x2(1 + -1i + x)) = 0 (2 + -2i + 2x + 2i + 2ix + -2i2 + 1ix + ix2 + -1i2x + -3ix + 3x + 3x2 + (1 * x2 + -1i * x2 + x * x2)) = 0 Reorder the terms: (2 + -2i + 2x + 2i + 2ix + -2i2 + 1ix + ix2 + -1i2x + -3ix + 3x + 3x2 + (-1ix2 + 1x2 + x3)) = 0 (2 + -2i + 2x + 2i + 2ix + -2i2 + 1ix + ix2 + -1i2x + -3ix + 3x + 3x2 + (-1ix2 + 1x2 + x3)) = 0 Reorder the terms: (2 + -2i + 2i + 2ix + 1ix + -3ix + ix2 + -1ix2 + -2i2 + -1i2x + 2x + 3x + 3x2 + 1x2 + x3) = 0 Combine like terms: -2i + 2i = 0 (2 + 0 + 2ix + 1ix + -3ix + ix2 + -1ix2 + -2i2 + -1i2x + 2x + 3x + 3x2 + 1x2 + x3) = 0 (2 + 2ix + 1ix + -3ix + ix2 + -1ix2 + -2i2 + -1i2x + 2x + 3x + 3x2 + 1x2 + x3) = 0 Combine like terms: 2ix + 1ix = 3ix (2 + 3ix + -3ix + ix2 + -1ix2 + -2i2 + -1i2x + 2x + 3x + 3x2 + 1x2 + x3) = 0 Combine like terms: 3ix + -3ix = 0 (2 + 0 + ix2 + -1ix2 + -2i2 + -1i2x + 2x + 3x + 3x2 + 1x2 + x3) = 0 (2 + ix2 + -1ix2 + -2i2 + -1i2x + 2x + 3x + 3x2 + 1x2 + x3) = 0 Combine like terms: ix2 + -1ix2 = 0 (2 + 0 + -2i2 + -1i2x + 2x + 3x + 3x2 + 1x2 + x3) = 0 (2 + -2i2 + -1i2x + 2x + 3x + 3x2 + 1x2 + x3) = 0 Combine like terms: 2x + 3x = 5x (2 + -2i2 + -1i2x + 5x + 3x2 + 1x2 + x3) = 0 Combine like terms: 3x2 + 1x2 = 4x2 (2 + -2i2 + -1i2x + 5x + 4x2 + x3) = 0 Solving 2 + -2i2 + -1i2x + 5x + 4x2 + x3 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2i2 + -1i2x + 5x + 4x2 + -2 + x3 = 0 + -2 Reorder the terms: 2 + -2 + -2i2 + -1i2x + 5x + 4x2 + x3 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -2i2 + -1i2x + 5x + 4x2 + x3 = 0 + -2 -2i2 + -1i2x + 5x + 4x2 + x3 = 0 + -2 Combine like terms: 0 + -2 = -2 -2i2 + -1i2x + 5x + 4x2 + x3 = -2 Add '-5x' to each side of the equation. -2i2 + -1i2x + 5x + 4x2 + -5x + x3 = -2 + -5x Reorder the terms: -2i2 + -1i2x + 5x + -5x + 4x2 + x3 = -2 + -5x Combine like terms: 5x + -5x = 0 -2i2 + -1i2x + 0 + 4x2 + x3 = -2 + -5x -2i2 + -1i2x + 4x2 + x3 = -2 + -5x Add '-4x2' to each side of the equation. -2i2 + -1i2x + 4x2 + -4x2 + x3 = -2 + -5x + -4x2 Combine like terms: 4x2 + -4x2 = 0 -2i2 + -1i2x + 0 + x3 = -2 + -5x + -4x2 -2i2 + -1i2x + x3 = -2 + -5x + -4x2 Add '-1x3' to each side of the equation. -2i2 + -1i2x + x3 + -1x3 = -2 + -5x + -4x2 + -1x3 Combine like terms: x3 + -1x3 = 0 -2i2 + -1i2x + 0 = -2 + -5x + -4x2 + -1x3 -2i2 + -1i2x = -2 + -5x + -4x2 + -1x3 Reorder the terms: 2 + -2i2 + -1i2x + 5x + 4x2 + x3 = -2 + -5x + -4x2 + -1x3 + 2 + 5x + 4x2 + x3 Reorder the terms: 2 + -2i2 + -1i2x + 5x + 4x2 + x3 = -2 + 2 + -5x + 5x + -4x2 + 4x2 + -1x3 + x3 Combine like terms: -2 + 2 = 0 2 + -2i2 + -1i2x + 5x + 4x2 + x3 = 0 + -5x + 5x + -4x2 + 4x2 + -1x3 + x3 2 + -2i2 + -1i2x + 5x + 4x2 + x3 = -5x + 5x + -4x2 + 4x2 + -1x3 + x3 Combine like terms: -5x + 5x = 0 2 + -2i2 + -1i2x + 5x + 4x2 + x3 = 0 + -4x2 + 4x2 + -1x3 + x3 2 + -2i2 + -1i2x + 5x + 4x2 + x3 = -4x2 + 4x2 + -1x3 + x3 Combine like terms: -4x2 + 4x2 = 0 2 + -2i2 + -1i2x + 5x + 4x2 + x3 = 0 + -1x3 + x3 2 + -2i2 + -1i2x + 5x + 4x2 + x3 = -1x3 + x3 Combine like terms: -1x3 + x3 = 0 2 + -2i2 + -1i2x + 5x + 4x2 + x3 = 0 The solution to this equation could not be determined.
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