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Simplifying (x + -1(1 + 2i))(x + -1(1 + -2i)) = 0 (x + (1 * -1 + 2i * -1))(x + -1(1 + -2i)) = 0 (x + (-1 + -2i))(x + -1(1 + -2i)) = 0 Reorder the terms: (-1 + -2i + x)(x + -1(1 + -2i)) = 0 (-1 + -2i + x)(x + (1 * -1 + -2i * -1)) = 0 (-1 + -2i + x)(x + (-1 + 2i)) = 0 Reorder the terms: (-1 + -2i + x)(-1 + 2i + x) = 0 Multiply (-1 + -2i + x) * (-1 + 2i + x) (-1(-1 + 2i + x) + -2i * (-1 + 2i + x) + x(-1 + 2i + x)) = 0 ((-1 * -1 + 2i * -1 + x * -1) + -2i * (-1 + 2i + x) + x(-1 + 2i + x)) = 0 ((1 + -2i + -1x) + -2i * (-1 + 2i + x) + x(-1 + 2i + x)) = 0 (1 + -2i + -1x + (-1 * -2i + 2i * -2i + x * -2i) + x(-1 + 2i + x)) = 0 Reorder the terms: (1 + -2i + -1x + (2i + -2ix + -4i2) + x(-1 + 2i + x)) = 0 (1 + -2i + -1x + (2i + -2ix + -4i2) + x(-1 + 2i + x)) = 0 (1 + -2i + -1x + 2i + -2ix + -4i2 + (-1 * x + 2i * x + x * x)) = 0 Reorder the terms: (1 + -2i + -1x + 2i + -2ix + -4i2 + (2ix + -1x + x2)) = 0 (1 + -2i + -1x + 2i + -2ix + -4i2 + (2ix + -1x + x2)) = 0 Reorder the terms: (1 + -2i + 2i + -2ix + 2ix + -4i2 + -1x + -1x + x2) = 0 Combine like terms: -2i + 2i = 0 (1 + 0 + -2ix + 2ix + -4i2 + -1x + -1x + x2) = 0 (1 + -2ix + 2ix + -4i2 + -1x + -1x + x2) = 0 Combine like terms: -2ix + 2ix = 0 (1 + 0 + -4i2 + -1x + -1x + x2) = 0 (1 + -4i2 + -1x + -1x + x2) = 0 Combine like terms: -1x + -1x = -2x (1 + -4i2 + -2x + x2) = 0 Solving 1 + -4i2 + -2x + x2 = 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 + -4i2 + -2x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -4i2 + -2x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4i2 + -2x + x2 = 0 + -1 -4i2 + -2x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -4i2 + -2x + x2 = -1 Add '2x' to each side of the equation. -4i2 + -2x + 2x + x2 = -1 + 2x Combine like terms: -2x + 2x = 0 -4i2 + 0 + x2 = -1 + 2x -4i2 + x2 = -1 + 2x Add '-1x2' to each side of the equation. -4i2 + x2 + -1x2 = -1 + 2x + -1x2 Combine like terms: x2 + -1x2 = 0 -4i2 + 0 = -1 + 2x + -1x2 -4i2 = -1 + 2x + -1x2 Divide each side by '-4'. i2 = 0.25 + -0.5x + 0.25x2 Simplifying i2 = 0.25 + -0.5x + 0.25x2 Reorder the terms: -0.25 + i2 + 0.5x + -0.25x2 = 0.25 + -0.5x + 0.25x2 + -0.25 + 0.5x + -0.25x2 Reorder the terms: -0.25 + i2 + 0.5x + -0.25x2 = 0.25 + -0.25 + -0.5x + 0.5x + 0.25x2 + -0.25x2 Combine like terms: 0.25 + -0.25 = 0.00 -0.25 + i2 + 0.5x + -0.25x2 = 0.00 + -0.5x + 0.5x + 0.25x2 + -0.25x2 -0.25 + i2 + 0.5x + -0.25x2 = -0.5x + 0.5x + 0.25x2 + -0.25x2 Combine like terms: -0.5x + 0.5x = 0.0 -0.25 + i2 + 0.5x + -0.25x2 = 0.0 + 0.25x2 + -0.25x2 -0.25 + i2 + 0.5x + -0.25x2 = 0.25x2 + -0.25x2 Combine like terms: 0.25x2 + -0.25x2 = 0.00 -0.25 + i2 + 0.5x + -0.25x2 = 0.00 The solution to this equation could not be determined.
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