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Simplifying (x + 3 + i)(x + 3 + -1i) = 0 Reorder the terms: (3 + i + x)(x + 3 + -1i) = 0 Reorder the terms: (3 + i + x)(3 + -1i + x) = 0 Multiply (3 + i + x) * (3 + -1i + x) (3(3 + -1i + x) + i(3 + -1i + x) + x(3 + -1i + x)) = 0 ((3 * 3 + -1i * 3 + x * 3) + i(3 + -1i + x) + x(3 + -1i + x)) = 0 ((9 + -3i + 3x) + i(3 + -1i + x) + x(3 + -1i + x)) = 0 (9 + -3i + 3x + (3 * i + -1i * i + x * i) + x(3 + -1i + x)) = 0 Reorder the terms: (9 + -3i + 3x + (3i + ix + -1i2) + x(3 + -1i + x)) = 0 (9 + -3i + 3x + (3i + ix + -1i2) + x(3 + -1i + x)) = 0 (9 + -3i + 3x + 3i + ix + -1i2 + (3 * x + -1i * x + x * x)) = 0 Reorder the terms: (9 + -3i + 3x + 3i + ix + -1i2 + (-1ix + 3x + x2)) = 0 (9 + -3i + 3x + 3i + ix + -1i2 + (-1ix + 3x + x2)) = 0 Reorder the terms: (9 + -3i + 3i + ix + -1ix + -1i2 + 3x + 3x + x2) = 0 Combine like terms: -3i + 3i = 0 (9 + 0 + ix + -1ix + -1i2 + 3x + 3x + x2) = 0 (9 + ix + -1ix + -1i2 + 3x + 3x + x2) = 0 Combine like terms: ix + -1ix = 0 (9 + 0 + -1i2 + 3x + 3x + x2) = 0 (9 + -1i2 + 3x + 3x + x2) = 0 Combine like terms: 3x + 3x = 6x (9 + -1i2 + 6x + x2) = 0 Solving 9 + -1i2 + 6x + x2 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -1i2 + 6x + -9 + x2 = 0 + -9 Reorder the terms: 9 + -9 + -1i2 + 6x + x2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1i2 + 6x + x2 = 0 + -9 -1i2 + 6x + x2 = 0 + -9 Combine like terms: 0 + -9 = -9 -1i2 + 6x + x2 = -9 Add '-6x' to each side of the equation. -1i2 + 6x + -6x + x2 = -9 + -6x Combine like terms: 6x + -6x = 0 -1i2 + 0 + x2 = -9 + -6x -1i2 + x2 = -9 + -6x Add '-1x2' to each side of the equation. -1i2 + x2 + -1x2 = -9 + -6x + -1x2 Combine like terms: x2 + -1x2 = 0 -1i2 + 0 = -9 + -6x + -1x2 -1i2 = -9 + -6x + -1x2 Divide each side by '-1'. i2 = 9 + 6x + x2 Simplifying i2 = 9 + 6x + x2 Reorder the terms: -9 + i2 + -6x + -1x2 = 9 + 6x + x2 + -9 + -6x + -1x2 Reorder the terms: -9 + i2 + -6x + -1x2 = 9 + -9 + 6x + -6x + x2 + -1x2 Combine like terms: 9 + -9 = 0 -9 + i2 + -6x + -1x2 = 0 + 6x + -6x + x2 + -1x2 -9 + i2 + -6x + -1x2 = 6x + -6x + x2 + -1x2 Combine like terms: 6x + -6x = 0 -9 + i2 + -6x + -1x2 = 0 + x2 + -1x2 -9 + i2 + -6x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -9 + i2 + -6x + -1x2 = 0 The solution to this equation could not be determined.
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