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Simplifying (x + -1(3 + i))(x + -1(3 + -1i)) = 0 (x + (3 * -1 + i * -1))(x + -1(3 + -1i)) = 0 (x + (-3 + -1i))(x + -1(3 + -1i)) = 0 Reorder the terms: (-3 + -1i + x)(x + -1(3 + -1i)) = 0 (-3 + -1i + x)(x + (3 * -1 + -1i * -1)) = 0 (-3 + -1i + x)(x + (-3 + 1i)) = 0 Reorder the terms: (-3 + -1i + x)(-3 + 1i + x) = 0 Multiply (-3 + -1i + x) * (-3 + 1i + x) (-3(-3 + 1i + x) + -1i * (-3 + 1i + x) + x(-3 + 1i + x)) = 0 ((-3 * -3 + 1i * -3 + x * -3) + -1i * (-3 + 1i + x) + x(-3 + 1i + x)) = 0 ((9 + -3i + -3x) + -1i * (-3 + 1i + x) + x(-3 + 1i + x)) = 0 (9 + -3i + -3x + (-3 * -1i + 1i * -1i + x * -1i) + x(-3 + 1i + x)) = 0 Reorder the terms: (9 + -3i + -3x + (3i + -1ix + -1i2) + x(-3 + 1i + x)) = 0 (9 + -3i + -3x + (3i + -1ix + -1i2) + x(-3 + 1i + x)) = 0 (9 + -3i + -3x + 3i + -1ix + -1i2 + (-3 * x + 1i * x + x * x)) = 0 Reorder the terms: (9 + -3i + -3x + 3i + -1ix + -1i2 + (1ix + -3x + x2)) = 0 (9 + -3i + -3x + 3i + -1ix + -1i2 + (1ix + -3x + x2)) = 0 Reorder the terms: (9 + -3i + 3i + -1ix + 1ix + -1i2 + -3x + -3x + x2) = 0 Combine like terms: -3i + 3i = 0 (9 + 0 + -1ix + 1ix + -1i2 + -3x + -3x + x2) = 0 (9 + -1ix + 1ix + -1i2 + -3x + -3x + x2) = 0 Combine like terms: -1ix + 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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