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Simplifying F(x) = (x + 2)(x + 3 + 3i)(x + 3 + -3i) Multiply F * x xF = (x + 2)(x + 3 + 3i)(x + 3 + -3i) Reorder the terms: xF = (2 + x)(x + 3 + 3i)(x + 3 + -3i) Reorder the terms: xF = (2 + x)(3 + 3i + x)(x + 3 + -3i) Reorder the terms: xF = (2 + x)(3 + 3i + x)(3 + -3i + x) Multiply (2 + x) * (3 + 3i + x) xF = (2(3 + 3i + x) + x(3 + 3i + x))(3 + -3i + x) xF = ((3 * 2 + 3i * 2 + x * 2) + x(3 + 3i + x))(3 + -3i + x) xF = ((6 + 6i + 2x) + x(3 + 3i + x))(3 + -3i + x) xF = (6 + 6i + 2x + (3 * x + 3i * x + x * x))(3 + -3i + x) Reorder the terms: xF = (6 + 6i + 2x + (3ix + 3x + x2))(3 + -3i + x) xF = (6 + 6i + 2x + (3ix + 3x + x2))(3 + -3i + x) Reorder the terms: xF = (6 + 6i + 3ix + 2x + 3x + x2)(3 + -3i + x) Combine like terms: 2x + 3x = 5x xF = (6 + 6i + 3ix + 5x + x2)(3 + -3i + x) Multiply (6 + 6i + 3ix + 5x + x2) * (3 + -3i + x) xF = (6(3 + -3i + x) + 6i * (3 + -3i + x) + 3ix * (3 + -3i + x) + 5x * (3 + -3i + x) + x2(3 + -3i + x)) xF = ((3 * 6 + -3i * 6 + x * 6) + 6i * (3 + -3i + x) + 3ix * (3 + -3i + x) + 5x * (3 + -3i + x) + x2(3 + -3i + x)) xF = ((18 + -18i + 6x) + 6i * (3 + -3i + x) + 3ix * (3 + -3i + x) + 5x * (3 + -3i + x) + x2(3 + -3i + x)) xF = (18 + -18i + 6x + (3 * 6i + -3i * 6i + x * 6i) + 3ix * (3 + -3i + x) + 5x * (3 + -3i + x) + x2(3 + -3i + x)) Reorder the terms: xF = (18 + -18i + 6x + (18i + 6ix + -18i2) + 3ix * (3 + -3i + x) + 5x * (3 + -3i + x) + x2(3 + -3i + x)) xF = (18 + -18i + 6x + (18i + 6ix + -18i2) + 3ix * (3 + -3i + x) + 5x * (3 + -3i + x) + x2(3 + -3i + x)) xF = (18 + -18i + 6x + 18i + 6ix + -18i2 + (3 * 3ix + -3i * 3ix + x * 3ix) + 5x * (3 + -3i + x) + x2(3 + -3i + x)) Reorder the terms: xF = (18 + -18i + 6x + 18i + 6ix + -18i2 + (9ix + 3ix2 + -9i2x) + 5x * (3 + -3i + x) + x2(3 + -3i + x)) xF = (18 + -18i + 6x + 18i + 6ix + -18i2 + (9ix + 3ix2 + -9i2x) + 5x * (3 + -3i + x) + x2(3 + -3i + x)) xF = (18 + -18i + 6x + 18i + 6ix + -18i2 + 9ix + 3ix2 + -9i2x + (3 * 5x + -3i * 5x + x * 5x) + x2(3 + -3i + x)) Reorder the terms: xF = (18 + -18i + 6x + 18i + 6ix + -18i2 + 9ix + 3ix2 + -9i2x + (-15ix + 15x + 5x2) + x2(3 + -3i + x)) xF = (18 + -18i + 6x + 18i + 6ix + -18i2 + 9ix + 3ix2 + -9i2x + (-15ix + 15x + 5x2) + x2(3 + -3i + x)) xF = (18 + -18i + 6x + 18i + 6ix + -18i2 + 9ix + 3ix2 + -9i2x + -15ix + 15x + 5x2 + (3 * x2 + -3i * x2 + x * x2)) Reorder the terms: xF = (18 + -18i + 6x + 18i + 6ix + -18i2 + 9ix + 3ix2 + -9i2x + -15ix + 15x + 5x2 + (-3ix2 + 3x2 + x3)) xF = (18 + -18i + 6x + 18i + 6ix + -18i2 + 9ix + 3ix2 + -9i2x + -15ix + 15x + 5x2 + (-3ix2 + 3x2 + x3)) Reorder the terms: xF = (18 + -18i + 18i + 6ix + 9ix + -15ix + 3ix2 + -3ix2 + -18i2 + -9i2x + 6x + 15x + 5x2 + 3x2 + x3) Combine like terms: -18i + 18i = 0 xF = (18 + 0 + 6ix + 9ix + -15ix + 3ix2 + -3ix2 + -18i2 + -9i2x + 6x + 15x + 5x2 + 3x2 + x3) xF = (18 + 6ix + 9ix + -15ix + 3ix2 + -3ix2 + -18i2 + -9i2x + 6x + 15x + 5x2 + 3x2 + x3) Combine like terms: 6ix + 9ix = 15ix xF = (18 + 15ix + -15ix + 3ix2 + -3ix2 + -18i2 + -9i2x + 6x + 15x + 5x2 + 3x2 + x3) Combine like terms: 15ix + -15ix = 0 xF = (18 + 0 + 3ix2 + -3ix2 + -18i2 + -9i2x + 6x + 15x + 5x2 + 3x2 + x3) xF = (18 + 3ix2 + -3ix2 + -18i2 + -9i2x + 6x + 15x + 5x2 + 3x2 + x3) Combine like terms: 3ix2 + -3ix2 = 0 xF = (18 + 0 + -18i2 + -9i2x + 6x + 15x + 5x2 + 3x2 + x3) xF = (18 + -18i2 + -9i2x + 6x + 15x + 5x2 + 3x2 + x3) Combine like terms: 6x + 15x = 21x xF = (18 + -18i2 + -9i2x + 21x + 5x2 + 3x2 + x3) Combine like terms: 5x2 + 3x2 = 8x2 xF = (18 + -18i2 + -9i2x + 21x + 8x2 + x3) Solving xF = 18 + -18i2 + -9i2x + 21x + 8x2 + x3 Solving for variable 'x'. Reorder the terms: -18 + 18i2 + 9i2x + -21x + xF + -8x2 + -1x3 = 18 + -18i2 + -9i2x + 21x + 8x2 + x3 + -18 + 18i2 + 9i2x + -21x + -8x2 + -1x3 Reorder the terms: -18 + 18i2 + 9i2x + -21x + xF + -8x2 + -1x3 = 18 + -18 + -18i2 + 18i2 + -9i2x + 9i2x + 21x + -21x + 8x2 + -8x2 + x3 + -1x3 Combine like terms: 18 + -18 = 0 -18 + 18i2 + 9i2x + -21x + xF + -8x2 + -1x3 = 0 + -18i2 + 18i2 + -9i2x + 9i2x + 21x + -21x + 8x2 + -8x2 + x3 + -1x3 -18 + 18i2 + 9i2x + -21x + xF + -8x2 + -1x3 = -18i2 + 18i2 + -9i2x + 9i2x + 21x + -21x + 8x2 + -8x2 + x3 + -1x3 Combine like terms: -18i2 + 18i2 = 0 -18 + 18i2 + 9i2x + -21x + xF + -8x2 + -1x3 = 0 + -9i2x + 9i2x + 21x + -21x + 8x2 + -8x2 + x3 + -1x3 -18 + 18i2 + 9i2x + -21x + xF + -8x2 + -1x3 = -9i2x + 9i2x + 21x + -21x + 8x2 + -8x2 + x3 + -1x3 Combine like terms: -9i2x + 9i2x = 0 -18 + 18i2 + 9i2x + -21x + xF + -8x2 + -1x3 = 0 + 21x + -21x + 8x2 + -8x2 + x3 + -1x3 -18 + 18i2 + 9i2x + -21x + xF + -8x2 + -1x3 = 21x + -21x + 8x2 + -8x2 + x3 + -1x3 Combine like terms: 21x + -21x = 0 -18 + 18i2 + 9i2x + -21x + xF + -8x2 + -1x3 = 0 + 8x2 + -8x2 + x3 + -1x3 -18 + 18i2 + 9i2x + -21x + xF + -8x2 + -1x3 = 8x2 + -8x2 + x3 + -1x3 Combine like terms: 8x2 + -8x2 = 0 -18 + 18i2 + 9i2x + -21x + xF + -8x2 + -1x3 = 0 + x3 + -1x3 -18 + 18i2 + 9i2x + -21x + xF + -8x2 + -1x3 = x3 + -1x3 Combine like terms: x3 + -1x3 = 0 -18 + 18i2 + 9i2x + -21x + xF + -8x2 + -1x3 = 0 The solution to this equation could not be determined.
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