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Simplifying 0 = (x + -2)(x + -2)(x + -4 + -1i)(x + -4 + i) Reorder the terms: 0 = (-2 + x)(x + -2)(x + -4 + -1i)(x + -4 + i) Reorder the terms: 0 = (-2 + x)(-2 + x)(x + -4 + -1i)(x + -4 + i) Reorder the terms: 0 = (-2 + x)(-2 + x)(-4 + -1i + x)(x + -4 + i) Reorder the terms: 0 = (-2 + x)(-2 + x)(-4 + -1i + x)(-4 + i + x) Multiply (-2 + x) * (-2 + x) 0 = (-2(-2 + x) + x(-2 + x))(-4 + -1i + x)(-4 + i + x) 0 = ((-2 * -2 + x * -2) + x(-2 + x))(-4 + -1i + x)(-4 + i + x) 0 = ((4 + -2x) + x(-2 + x))(-4 + -1i + x)(-4 + i + x) 0 = (4 + -2x + (-2 * x + x * x))(-4 + -1i + x)(-4 + i + x) 0 = (4 + -2x + (-2x + x2))(-4 + -1i + x)(-4 + i + x) Combine like terms: -2x + -2x = -4x 0 = (4 + -4x + x2)(-4 + -1i + x)(-4 + i + x) Multiply (4 + -4x + x2) * (-4 + -1i + x) 0 = (4(-4 + -1i + x) + -4x * (-4 + -1i + x) + x2(-4 + -1i + x))(-4 + i + x) 0 = ((-4 * 4 + -1i * 4 + x * 4) + -4x * (-4 + -1i + x) + x2(-4 + -1i + x))(-4 + i + x) 0 = ((-16 + -4i + 4x) + -4x * (-4 + -1i + x) + x2(-4 + -1i + x))(-4 + i + x) 0 = (-16 + -4i + 4x + (-4 * -4x + -1i * -4x + x * -4x) + x2(-4 + -1i + x))(-4 + i + x) Reorder the terms: 0 = (-16 + -4i + 4x + (4ix + 16x + -4x2) + x2(-4 + -1i + x))(-4 + i + x) 0 = (-16 + -4i + 4x + (4ix + 16x + -4x2) + x2(-4 + -1i + x))(-4 + i + x) 0 = (-16 + -4i + 4x + 4ix + 16x + -4x2 + (-4 * x2 + -1i * x2 + x * x2))(-4 + i + x) Reorder the terms: 0 = (-16 + -4i + 4x + 4ix + 16x + -4x2 + (-1ix2 + -4x2 + x3))(-4 + i + x) 0 = (-16 + -4i + 4x + 4ix + 16x + -4x2 + (-1ix2 + -4x2 + x3))(-4 + i + x) Reorder the terms: 0 = (-16 + -4i + 4ix + -1ix2 + 4x + 16x + -4x2 + -4x2 + x3)(-4 + i + x) Combine like terms: 4x + 16x = 20x 0 = (-16 + -4i + 4ix + -1ix2 + 20x + -4x2 + -4x2 + x3)(-4 + i + x) Combine like terms: -4x2 + -4x2 = -8x2 0 = (-16 + -4i + 4ix + -1ix2 + 20x + -8x2 + x3)(-4 + i + x) Multiply (-16 + -4i + 4ix + -1ix2 + 20x + -8x2 + x3) * (-4 + i + x) 0 = (-16(-4 + i + x) + -4i * (-4 + i + x) + 4ix * (-4 + i + x) + -1ix2 * (-4 + i + x) + 20x * (-4 + i + x) + -8x2 * (-4 + i + x) + x3(-4 + i + x)) 0 = ((-4 * -16 + i * -16 + x * -16) + -4i * (-4 + i + x) + 4ix * (-4 + i + x) + -1ix2 * (-4 + i + x) + 20x * (-4 + i + x) + -8x2 * (-4 + i + x) + x3(-4 + i + x)) 0 = ((64 + -16i + -16x) + -4i * (-4 + i + x) + 4ix * (-4 + i + x) + -1ix2 * (-4 + i + x) + 20x * (-4 + i + x) + -8x2 * (-4 + i + x) + x3(-4 + i + x)) 0 = (64 + -16i + -16x + (-4 * -4i + i * -4i + x * -4i) + 4ix * (-4 + i + x) + -1ix2 * (-4 + i + x) + 20x * (-4 + i + x) + -8x2 * (-4 + i + x) + x3(-4 + i + x)) Reorder the terms: 0 = (64 + -16i + -16x + (16i + -4ix + -4i2) + 4ix * (-4 + i + x) + -1ix2 * (-4 + i + x) + 20x * (-4 + i + x) + -8x2 * (-4 + i + x) + x3(-4 + i + x)) 0 = (64 + -16i + -16x + (16i + -4ix + -4i2) + 4ix * (-4 + i + x) + -1ix2 * (-4 + i + x) + 20x * (-4 + i + x) + -8x2 * (-4 + i + x) + x3(-4 + i + x)) 0 = (64 + -16i + -16x + 16i + -4ix + -4i2 + (-4 * 4ix + i * 4ix + x * 4ix) + -1ix2 * (-4 + i + x) + 20x * (-4 + i + x) + -8x2 * (-4 + i + x) + x3(-4 + i + x)) Reorder the terms: 0 = (64 + -16i + -16x + 16i + -4ix + -4i2 + (-16ix + 4ix2 + 4i2x) + -1ix2 * (-4 + i + x) + 20x * (-4 + i + x) + -8x2 * (-4 + i + x) + x3(-4 + i + x)) 0 = (64 + -16i + -16x + 16i + -4ix + -4i2 + (-16ix + 4ix2 + 4i2x) + -1ix2 * (-4 + i + x) + 20x * (-4 + i + x) + -8x2 * (-4 + i + x) + x3(-4 + i + x)) 0 = (64 + -16i + -16x + 16i + -4ix + -4i2 + -16ix + 4ix2 + 4i2x + (-4 * -1ix2 + i * -1ix2 + x * -1ix2) + 20x * (-4 + i + x) + -8x2 * (-4 + i + x) + x3(-4 + i + x)) Reorder the terms: 0 = (64 + -16i + -16x + 16i + -4ix + -4i2 + -16ix + 4ix2 + 4i2x + (4ix2 + -1ix3 + -1i2x2) + 20x * (-4 + i + x) + -8x2 * (-4 + i + x) + x3(-4 + i + x)) 0 = (64 + -16i + -16x + 16i + -4ix + -4i2 + -16ix + 4ix2 + 4i2x + (4ix2 + -1ix3 + -1i2x2) + 20x * (-4 + i + x) + -8x2 * (-4 + i + x) + x3(-4 + i + x)) 0 = (64 + -16i + -16x + 16i + -4ix + -4i2 + -16ix + 4ix2 + 4i2x + 4ix2 + -1ix3 + -1i2x2 + (-4 * 20x + i * 20x + x * 20x) + -8x2 * (-4 + i + x) + x3(-4 + i + x)) Reorder the terms: 0 = (64 + -16i + -16x + 16i + -4ix + -4i2 + -16ix + 4ix2 + 4i2x + 4ix2 + -1ix3 + -1i2x2 + (20ix + -80x + 20x2) + -8x2 * (-4 + i + x) + x3(-4 + i + x)) 0 = (64 + -16i + -16x + 16i + -4ix + -4i2 + -16ix + 4ix2 + 4i2x + 4ix2 + -1ix3 + -1i2x2 + (20ix + -80x + 20x2) + -8x2 * (-4 + i + x) + x3(-4 + i + x)) 0 = (64 + -16i + -16x + 16i + -4ix + -4i2 + -16ix + 4ix2 + 4i2x + 4ix2 + -1ix3 + -1i2x2 + 20ix + -80x + 20x2 + (-4 * -8x2 + i * -8x2 + x * -8x2) + x3(-4 + i + x)) Reorder the terms: 0 = (64 + -16i + -16x + 16i + -4ix + -4i2 + -16ix + 4ix2 + 4i2x + 4ix2 + -1ix3 + -1i2x2 + 20ix + -80x + 20x2 + (-8ix2 + 32x2 + -8x3) + x3(-4 + i + x)) 0 = (64 + -16i + -16x + 16i + -4ix + -4i2 + -16ix + 4ix2 + 4i2x + 4ix2 + -1ix3 + -1i2x2 + 20ix + -80x + 20x2 + (-8ix2 + 32x2 + -8x3) + x3(-4 + i + x)) 0 = (64 + -16i + -16x + 16i + -4ix + -4i2 + -16ix + 4ix2 + 4i2x + 4ix2 + -1ix3 + -1i2x2 + 20ix + -80x + 20x2 + -8ix2 + 32x2 + -8x3 + (-4 * x3 + i * x3 + x * x3)) Reorder the terms: 0 = (64 + -16i + -16x + 16i + -4ix + -4i2 + -16ix + 4ix2 + 4i2x + 4ix2 + -1ix3 + -1i2x2 + 20ix + -80x + 20x2 + -8ix2 + 32x2 + -8x3 + (ix3 + -4x3 + x4)) 0 = (64 + -16i + -16x + 16i + -4ix + -4i2 + -16ix + 4ix2 + 4i2x + 4ix2 + -1ix3 + -1i2x2 + 20ix + -80x + 20x2 + -8ix2 + 32x2 + -8x3 + (ix3 + -4x3 + x4)) Reorder the terms: 0 = (64 + -16i + 16i + -4ix + -16ix + 20ix + 4ix2 + 4ix2 + -8ix2 + -1ix3 + ix3 + -4i2 + 4i2x + -1i2x2 + -16x + -80x + 20x2 + 32x2 + -8x3 + -4x3 + x4) Combine like terms: -16i + 16i = 0 0 = (64 + 0 + -4ix + -16ix + 20ix + 4ix2 + 4ix2 + -8ix2 + -1ix3 + ix3 + -4i2 + 4i2x + -1i2x2 + -16x + -80x + 20x2 + 32x2 + -8x3 + -4x3 + x4) 0 = (64 + -4ix + -16ix + 20ix + 4ix2 + 4ix2 + -8ix2 + -1ix3 + ix3 + -4i2 + 4i2x + -1i2x2 + -16x + -80x + 20x2 + 32x2 + -8x3 + -4x3 + x4) Combine like terms: -4ix + -16ix = -20ix 0 = (64 + -20ix + 20ix + 4ix2 + 4ix2 + -8ix2 + -1ix3 + ix3 + -4i2 + 4i2x + -1i2x2 + -16x + -80x + 20x2 + 32x2 + -8x3 + -4x3 + x4) Combine like terms: -20ix + 20ix = 0 0 = (64 + 0 + 4ix2 + 4ix2 + -8ix2 + -1ix3 + ix3 + -4i2 + 4i2x + -1i2x2 + -16x + -80x + 20x2 + 32x2 + -8x3 + -4x3 + x4) 0 = (64 + 4ix2 + 4ix2 + -8ix2 + -1ix3 + ix3 + -4i2 + 4i2x + -1i2x2 + -16x + -80x + 20x2 + 32x2 + -8x3 + -4x3 + x4) Combine like terms: 4ix2 + 4ix2 = 8ix2 0 = (64 + 8ix2 + -8ix2 + -1ix3 + ix3 + -4i2 + 4i2x + -1i2x2 + -16x + -80x + 20x2 + 32x2 + -8x3 + -4x3 + x4) Combine like terms: 8ix2 + -8ix2 = 0 0 = (64 + 0 + -1ix3 + ix3 + -4i2 + 4i2x + -1i2x2 + -16x + -80x + 20x2 + 32x2 + -8x3 + -4x3 + x4) 0 = (64 + -1ix3 + ix3 + -4i2 + 4i2x + -1i2x2 + -16x + -80x + 20x2 + 32x2 + -8x3 + -4x3 + x4) Combine like terms: -1ix3 + ix3 = 0 0 = (64 + 0 + -4i2 + 4i2x + -1i2x2 + -16x + -80x + 20x2 + 32x2 + -8x3 + -4x3 + x4) 0 = (64 + -4i2 + 4i2x + -1i2x2 + -16x + -80x + 20x2 + 32x2 + -8x3 + -4x3 + x4) Combine like terms: -16x + -80x = -96x 0 = (64 + -4i2 + 4i2x + -1i2x2 + -96x + 20x2 + 32x2 + -8x3 + -4x3 + x4) Combine like terms: 20x2 + 32x2 = 52x2 0 = (64 + -4i2 + 4i2x + -1i2x2 + -96x + 52x2 + -8x3 + -4x3 + x4) Combine like terms: -8x3 + -4x3 = -12x3 0 = (64 + -4i2 + 4i2x + -1i2x2 + -96x + 52x2 + -12x3 + x4) Solving 0 = 64 + -4i2 + 4i2x + -1i2x2 + -96x + 52x2 + -12x3 + x4 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '4i2' to each side of the equation. 0 + 4i2 = 64 + -4i2 + 4i2x + -1i2x2 + -96x + 52x2 + -12x3 + 4i2 + x4 Remove the zero: 4i2 = 64 + -4i2 + 4i2x + -1i2x2 + -96x + 52x2 + -12x3 + 4i2 + x4 Reorder the terms: 4i2 = 64 + -4i2 + 4i2 + 4i2x + -1i2x2 + -96x + 52x2 + -12x3 + x4 Combine like terms: -4i2 + 4i2 = 0 4i2 = 64 + 0 + 4i2x + -1i2x2 + -96x + 52x2 + -12x3 + x4 4i2 = 64 + 4i2x + -1i2x2 + -96x + 52x2 + -12x3 + x4 Add '-4i2x' to each side of the equation. 4i2 + -4i2x = 64 + 4i2x + -1i2x2 + -96x + 52x2 + -12x3 + -4i2x + x4 Reorder the terms: 4i2 + -4i2x = 64 + 4i2x + -4i2x + -1i2x2 + -96x + 52x2 + -12x3 + x4 Combine like terms: 4i2x + -4i2x = 0 4i2 + -4i2x = 64 + 0 + -1i2x2 + -96x + 52x2 + -12x3 + x4 4i2 + -4i2x = 64 + -1i2x2 + -96x + 52x2 + -12x3 + x4 Add 'i2x2' to each side of the equation. 4i2 + -4i2x + i2x2 = 64 + -1i2x2 + -96x + 52x2 + -12x3 + i2x2 + x4 Reorder the terms: 4i2 + -4i2x + i2x2 = 64 + -1i2x2 + i2x2 + -96x + 52x2 + -12x3 + x4 Combine like terms: -1i2x2 + i2x2 = 0 4i2 + -4i2x + i2x2 = 64 + 0 + -96x + 52x2 + -12x3 + x4 4i2 + -4i2x + i2x2 = 64 + -96x + 52x2 + -12x3 + x4 Reorder the terms: -64 + 4i2 + -4i2x + i2x2 + 96x + -52x2 + 12x3 + -1x4 = 64 + -96x + 52x2 + -12x3 + x4 + -64 + 96x + -52x2 + 12x3 + -1x4 Reorder the terms: -64 + 4i2 + -4i2x + i2x2 + 96x + -52x2 + 12x3 + -1x4 = 64 + -64 + -96x + 96x + 52x2 + -52x2 + -12x3 + 12x3 + x4 + -1x4 Combine like terms: 64 + -64 = 0 -64 + 4i2 + -4i2x + i2x2 + 96x + -52x2 + 12x3 + -1x4 = 0 + -96x + 96x + 52x2 + -52x2 + -12x3 + 12x3 + x4 + -1x4 -64 + 4i2 + -4i2x + i2x2 + 96x + -52x2 + 12x3 + -1x4 = -96x + 96x + 52x2 + -52x2 + -12x3 + 12x3 + x4 + -1x4 Combine like terms: -96x + 96x = 0 -64 + 4i2 + -4i2x + i2x2 + 96x + -52x2 + 12x3 + -1x4 = 0 + 52x2 + -52x2 + -12x3 + 12x3 + x4 + -1x4 -64 + 4i2 + -4i2x + i2x2 + 96x + -52x2 + 12x3 + -1x4 = 52x2 + -52x2 + -12x3 + 12x3 + x4 + -1x4 Combine like terms: 52x2 + -52x2 = 0 -64 + 4i2 + -4i2x + i2x2 + 96x + -52x2 + 12x3 + -1x4 = 0 + -12x3 + 12x3 + x4 + -1x4 -64 + 4i2 + -4i2x + i2x2 + 96x + -52x2 + 12x3 + -1x4 = -12x3 + 12x3 + x4 + -1x4 Combine like terms: -12x3 + 12x3 = 0 -64 + 4i2 + -4i2x + i2x2 + 96x + -52x2 + 12x3 + -1x4 = 0 + x4 + -1x4 -64 + 4i2 + -4i2x + i2x2 + 96x + -52x2 + 12x3 + -1x4 = x4 + -1x4 Combine like terms: x4 + -1x4 = 0 -64 + 4i2 + -4i2x + i2x2 + 96x + -52x2 + 12x3 + -1x4 = 0 The solution to this equation could not be determined.
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