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Simplifying (x + -2 + -1i)(x + -2 + i) = 0 Reorder the terms: (-2 + -1i + x)(x + -2 + i) = 0 Reorder the terms: (-2 + -1i + x)(-2 + i + x) = 0 Multiply (-2 + -1i + x) * (-2 + i + x) (-2(-2 + i + x) + -1i * (-2 + i + x) + x(-2 + i + x)) = 0 ((-2 * -2 + i * -2 + x * -2) + -1i * (-2 + i + x) + x(-2 + i + x)) = 0 ((4 + -2i + -2x) + -1i * (-2 + i + x) + x(-2 + i + x)) = 0 (4 + -2i + -2x + (-2 * -1i + i * -1i + x * -1i) + x(-2 + i + x)) = 0 Reorder the terms: (4 + -2i + -2x + (2i + -1ix + -1i2) + x(-2 + i + x)) = 0 (4 + -2i + -2x + (2i + -1ix + -1i2) + x(-2 + i + x)) = 0 (4 + -2i + -2x + 2i + -1ix + -1i2 + (-2 * x + i * x + x * x)) = 0 Reorder the terms: (4 + -2i + -2x + 2i + -1ix + -1i2 + (ix + -2x + x2)) = 0 (4 + -2i + -2x + 2i + -1ix + -1i2 + (ix + -2x + x2)) = 0 Reorder the terms: (4 + -2i + 2i + -1ix + ix + -1i2 + -2x + -2x + x2) = 0 Combine like terms: -2i + 2i = 0 (4 + 0 + -1ix + ix + -1i2 + -2x + -2x + x2) = 0 (4 + -1ix + ix + -1i2 + -2x + -2x + x2) = 0 Combine like terms: -1ix + ix = 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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