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Simplifying (x + -1(2 + 3i))(x + -1(2 + -3i)) = 0 (x + (2 * -1 + 3i * -1))(x + -1(2 + -3i)) = 0 (x + (-2 + -3i))(x + -1(2 + -3i)) = 0 Reorder the terms: (-2 + -3i + x)(x + -1(2 + -3i)) = 0 (-2 + -3i + x)(x + (2 * -1 + -3i * -1)) = 0 (-2 + -3i + x)(x + (-2 + 3i)) = 0 Reorder the terms: (-2 + -3i + x)(-2 + 3i + x) = 0 Multiply (-2 + -3i + x) * (-2 + 3i + x) (-2(-2 + 3i + x) + -3i * (-2 + 3i + x) + x(-2 + 3i + x)) = 0 ((-2 * -2 + 3i * -2 + x * -2) + -3i * (-2 + 3i + x) + x(-2 + 3i + x)) = 0 ((4 + -6i + -2x) + -3i * (-2 + 3i + x) + x(-2 + 3i + x)) = 0 (4 + -6i + -2x + (-2 * -3i + 3i * -3i + x * -3i) + x(-2 + 3i + x)) = 0 Reorder the terms: (4 + -6i + -2x + (6i + -3ix + -9i2) + x(-2 + 3i + x)) = 0 (4 + -6i + -2x + (6i + -3ix + -9i2) + x(-2 + 3i + x)) = 0 (4 + -6i + -2x + 6i + -3ix + -9i2 + (-2 * x + 3i * x + x * x)) = 0 Reorder the terms: (4 + -6i + -2x + 6i + -3ix + -9i2 + (3ix + -2x + x2)) = 0 (4 + -6i + -2x + 6i + -3ix + -9i2 + (3ix + -2x + x2)) = 0 Reorder the terms: (4 + -6i + 6i + -3ix + 3ix + -9i2 + -2x + -2x + x2) = 0 Combine like terms: -6i + 6i = 0 (4 + 0 + -3ix + 3ix + -9i2 + -2x + -2x + x2) = 0 (4 + -3ix + 3ix + -9i2 + -2x + -2x + x2) = 0 Combine like terms: -3ix + 3ix = 0 (4 + 0 + -9i2 + -2x + -2x + x2) = 0 (4 + -9i2 + -2x + -2x + x2) = 0 Combine like terms: -2x + -2x = -4x (4 + -9i2 + -4x + x2) = 0 Solving 4 + -9i2 + -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 + -9i2 + -4x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + -9i2 + -4x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -9i2 + -4x + x2 = 0 + -4 -9i2 + -4x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -9i2 + -4x + x2 = -4 Add '4x' to each side of the equation. -9i2 + -4x + 4x + x2 = -4 + 4x Combine like terms: -4x + 4x = 0 -9i2 + 0 + x2 = -4 + 4x -9i2 + x2 = -4 + 4x Add '-1x2' to each side of the equation. -9i2 + x2 + -1x2 = -4 + 4x + -1x2 Combine like terms: x2 + -1x2 = 0 -9i2 + 0 = -4 + 4x + -1x2 -9i2 = -4 + 4x + -1x2 Divide each side by '-9'. i2 = 0.4444444444 + -0.4444444444x + 0.1111111111x2 Simplifying i2 = 0.4444444444 + -0.4444444444x + 0.1111111111x2 Reorder the terms: -0.4444444444 + i2 + 0.4444444444x + -0.1111111111x2 = 0.4444444444 + -0.4444444444x + 0.1111111111x2 + -0.4444444444 + 0.4444444444x + -0.1111111111x2 Reorder the terms: -0.4444444444 + i2 + 0.4444444444x + -0.1111111111x2 = 0.4444444444 + -0.4444444444 + -0.4444444444x + 0.4444444444x + 0.1111111111x2 + -0.1111111111x2 Combine like terms: 0.4444444444 + -0.4444444444 = 0.0000000000 -0.4444444444 + i2 + 0.4444444444x + -0.1111111111x2 = 0.0000000000 + -0.4444444444x + 0.4444444444x + 0.1111111111x2 + -0.1111111111x2 -0.4444444444 + i2 + 0.4444444444x + -0.1111111111x2 = -0.4444444444x + 0.4444444444x + 0.1111111111x2 + -0.1111111111x2 Combine like terms: -0.4444444444x + 0.4444444444x = 0.0000000000 -0.4444444444 + i2 + 0.4444444444x + -0.1111111111x2 = 0.0000000000 + 0.1111111111x2 + -0.1111111111x2 -0.4444444444 + i2 + 0.4444444444x + -0.1111111111x2 = 0.1111111111x2 + -0.1111111111x2 Combine like terms: 0.1111111111x2 + -0.1111111111x2 = 0.0000000000 -0.4444444444 + i2 + 0.4444444444x + -0.1111111111x2 = 0.0000000000 The solution to this equation could not be determined.
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