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Simplifying (x + 3i + 1)(x + -3i + 1) = 0 Reorder the terms: (1 + 3i + x)(x + -3i + 1) = 0 Reorder the terms: (1 + 3i + x)(1 + -3i + x) = 0 Multiply (1 + 3i + x) * (1 + -3i + x) (1(1 + -3i + x) + 3i * (1 + -3i + x) + x(1 + -3i + x)) = 0 ((1 * 1 + -3i * 1 + x * 1) + 3i * (1 + -3i + x) + x(1 + -3i + x)) = 0 ((1 + -3i + 1x) + 3i * (1 + -3i + x) + x(1 + -3i + x)) = 0 (1 + -3i + 1x + (1 * 3i + -3i * 3i + x * 3i) + x(1 + -3i + x)) = 0 Reorder the terms: (1 + -3i + 1x + (3i + 3ix + -9i2) + x(1 + -3i + x)) = 0 (1 + -3i + 1x + (3i + 3ix + -9i2) + x(1 + -3i + x)) = 0 (1 + -3i + 1x + 3i + 3ix + -9i2 + (1 * x + -3i * x + x * x)) = 0 Reorder the terms: (1 + -3i + 1x + 3i + 3ix + -9i2 + (-3ix + 1x + x2)) = 0 (1 + -3i + 1x + 3i + 3ix + -9i2 + (-3ix + 1x + x2)) = 0 Reorder the terms: (1 + -3i + 3i + 3ix + -3ix + -9i2 + 1x + 1x + x2) = 0 Combine like terms: -3i + 3i = 0 (1 + 0 + 3ix + -3ix + -9i2 + 1x + 1x + x2) = 0 (1 + 3ix + -3ix + -9i2 + 1x + 1x + x2) = 0 Combine like terms: 3ix + -3ix = 0 (1 + 0 + -9i2 + 1x + 1x + x2) = 0 (1 + -9i2 + 1x + 1x + x2) = 0 Combine like terms: 1x + 1x = 2x (1 + -9i2 + 2x + x2) = 0 Solving 1 + -9i2 + 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 + -9i2 + 2x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -9i2 + 2x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -9i2 + 2x + x2 = 0 + -1 -9i2 + 2x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -9i2 + 2x + x2 = -1 Add '-2x' to each side of the equation. -9i2 + 2x + -2x + x2 = -1 + -2x Combine like terms: 2x + -2x = 0 -9i2 + 0 + x2 = -1 + -2x -9i2 + x2 = -1 + -2x Add '-1x2' to each side of the equation. -9i2 + x2 + -1x2 = -1 + -2x + -1x2 Combine like terms: x2 + -1x2 = 0 -9i2 + 0 = -1 + -2x + -1x2 -9i2 = -1 + -2x + -1x2 Divide each side by '-9'. i2 = 0.1111111111 + 0.2222222222x + 0.1111111111x2 Simplifying i2 = 0.1111111111 + 0.2222222222x + 0.1111111111x2 Reorder the terms: -0.1111111111 + i2 + -0.2222222222x + -0.1111111111x2 = 0.1111111111 + 0.2222222222x + 0.1111111111x2 + -0.1111111111 + -0.2222222222x + -0.1111111111x2 Reorder the terms: -0.1111111111 + i2 + -0.2222222222x + -0.1111111111x2 = 0.1111111111 + -0.1111111111 + 0.2222222222x + -0.2222222222x + 0.1111111111x2 + -0.1111111111x2 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 -0.1111111111 + i2 + -0.2222222222x + -0.1111111111x2 = 0.0000000000 + 0.2222222222x + -0.2222222222x + 0.1111111111x2 + -0.1111111111x2 -0.1111111111 + i2 + -0.2222222222x + -0.1111111111x2 = 0.2222222222x + -0.2222222222x + 0.1111111111x2 + -0.1111111111x2 Combine like terms: 0.2222222222x + -0.2222222222x = 0.0000000000 -0.1111111111 + i2 + -0.2222222222x + -0.1111111111x2 = 0.0000000000 + 0.1111111111x2 + -0.1111111111x2 -0.1111111111 + i2 + -0.2222222222x + -0.1111111111x2 = 0.1111111111x2 + -0.1111111111x2 Combine like terms: 0.1111111111x2 + -0.1111111111x2 = 0.0000000000 -0.1111111111 + i2 + -0.2222222222x + -0.1111111111x2 = 0.0000000000 The solution to this equation could not be determined.
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