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Simplifying (x + -1(4 + i))(x + -1(4 + i))(x + -1) = 0 (x + (4 * -1 + i * -1))(x + -1(4 + i))(x + -1) = 0 (x + (-4 + -1i))(x + -1(4 + i))(x + -1) = 0 Reorder the terms: (-4 + -1i + x)(x + -1(4 + i))(x + -1) = 0 (-4 + -1i + x)(x + (4 * -1 + i * -1))(x + -1) = 0 (-4 + -1i + x)(x + (-4 + -1i))(x + -1) = 0 Reorder the terms: (-4 + -1i + x)(-4 + -1i + x)(x + -1) = 0 Reorder the terms: (-4 + -1i + x)(-4 + -1i + x)(-1 + x) = 0 Multiply (-4 + -1i + x) * (-4 + -1i + x) (-4(-4 + -1i + x) + -1i * (-4 + -1i + x) + x(-4 + -1i + x))(-1 + x) = 0 ((-4 * -4 + -1i * -4 + x * -4) + -1i * (-4 + -1i + x) + x(-4 + -1i + x))(-1 + x) = 0 ((16 + 4i + -4x) + -1i * (-4 + -1i + x) + x(-4 + -1i + x))(-1 + x) = 0 (16 + 4i + -4x + (-4 * -1i + -1i * -1i + x * -1i) + x(-4 + -1i + x))(-1 + x) = 0 Reorder the terms: (16 + 4i + -4x + (4i + -1ix + 1i2) + x(-4 + -1i + x))(-1 + x) = 0 (16 + 4i + -4x + (4i + -1ix + 1i2) + x(-4 + -1i + x))(-1 + x) = 0 (16 + 4i + -4x + 4i + -1ix + 1i2 + (-4 * x + -1i * x + x * x))(-1 + x) = 0 Reorder the terms: (16 + 4i + -4x + 4i + -1ix + 1i2 + (-1ix + -4x + x2))(-1 + x) = 0 (16 + 4i + -4x + 4i + -1ix + 1i2 + (-1ix + -4x + x2))(-1 + x) = 0 Reorder the terms: (16 + 4i + 4i + -1ix + -1ix + 1i2 + -4x + -4x + x2)(-1 + x) = 0 Combine like terms: 4i + 4i = 8i (16 + 8i + -1ix + -1ix + 1i2 + -4x + -4x + x2)(-1 + x) = 0 Combine like terms: -1ix + -1ix = -2ix (16 + 8i + -2ix + 1i2 + -4x + -4x + x2)(-1 + x) = 0 Combine like terms: -4x + -4x = -8x (16 + 8i + -2ix + 1i2 + -8x + x2)(-1 + x) = 0 Multiply (16 + 8i + -2ix + 1i2 + -8x + x2) * (-1 + x) (16(-1 + x) + 8i * (-1 + x) + -2ix * (-1 + x) + 1i2 * (-1 + x) + -8x * (-1 + x) + x2(-1 + x)) = 0 ((-1 * 16 + x * 16) + 8i * (-1 + x) + -2ix * (-1 + x) + 1i2 * (-1 + x) + -8x * (-1 + x) + x2(-1 + x)) = 0 ((-16 + 16x) + 8i * (-1 + x) + -2ix * (-1 + x) + 1i2 * (-1 + x) + -8x * (-1 + x) + x2(-1 + x)) = 0 (-16 + 16x + (-1 * 8i + x * 8i) + -2ix * (-1 + x) + 1i2 * (-1 + x) + -8x * (-1 + x) + x2(-1 + x)) = 0 (-16 + 16x + (-8i + 8ix) + -2ix * (-1 + x) + 1i2 * (-1 + x) + -8x * (-1 + x) + x2(-1 + x)) = 0 (-16 + 16x + -8i + 8ix + (-1 * -2ix + x * -2ix) + 1i2 * (-1 + x) + -8x * (-1 + x) + x2(-1 + x)) = 0 (-16 + 16x + -8i + 8ix + (2ix + -2ix2) + 1i2 * (-1 + x) + -8x * (-1 + x) + x2(-1 + x)) = 0 (-16 + 16x + -8i + 8ix + 2ix + -2ix2 + (-1 * 1i2 + x * 1i2) + -8x * (-1 + x) + x2(-1 + x)) = 0 (-16 + 16x + -8i + 8ix + 2ix + -2ix2 + (-1i2 + 1i2x) + -8x * (-1 + x) + x2(-1 + x)) = 0 (-16 + 16x + -8i + 8ix + 2ix + -2ix2 + -1i2 + 1i2x + (-1 * -8x + x * -8x) + x2(-1 + x)) = 0 (-16 + 16x + -8i + 8ix + 2ix + -2ix2 + -1i2 + 1i2x + (8x + -8x2) + x2(-1 + x)) = 0 (-16 + 16x + -8i + 8ix + 2ix + -2ix2 + -1i2 + 1i2x + 8x + -8x2 + (-1 * x2 + x * x2)) = 0 (-16 + 16x + -8i + 8ix + 2ix + -2ix2 + -1i2 + 1i2x + 8x + -8x2 + (-1x2 + x3)) = 0 Reorder the terms: (-16 + -8i + 8ix + 2ix + -2ix2 + -1i2 + 1i2x + 16x + 8x + -8x2 + -1x2 + x3) = 0 Combine like terms: 8ix + 2ix = 10ix (-16 + -8i + 10ix + -2ix2 + -1i2 + 1i2x + 16x + 8x + -8x2 + -1x2 + x3) = 0 Combine like terms: 16x + 8x = 24x (-16 + -8i + 10ix + -2ix2 + -1i2 + 1i2x + 24x + -8x2 + -1x2 + x3) = 0 Combine like terms: -8x2 + -1x2 = -9x2 (-16 + -8i + 10ix + -2ix2 + -1i2 + 1i2x + 24x + -9x2 + x3) = 0 Solving -16 + -8i + 10ix + -2ix2 + -1i2 + 1i2x + 24x + -9x2 + x3 = 0 Solving for variable 'i'. The solution to this equation could not be determined.
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