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Simplifying (x + 2)(x + -1(4 + -4i))(x + -1(4 + 4i)) = 0 Reorder the terms: (2 + x)(x + -1(4 + -4i))(x + -1(4 + 4i)) = 0 (2 + x)(x + (4 * -1 + -4i * -1))(x + -1(4 + 4i)) = 0 (2 + x)(x + (-4 + 4i))(x + -1(4 + 4i)) = 0 Reorder the terms: (2 + x)(-4 + 4i + x)(x + -1(4 + 4i)) = 0 (2 + x)(-4 + 4i + x)(x + (4 * -1 + 4i * -1)) = 0 (2 + x)(-4 + 4i + x)(x + (-4 + -4i)) = 0 Reorder the terms: (2 + x)(-4 + 4i + x)(-4 + -4i + x) = 0 Multiply (2 + x) * (-4 + 4i + x) (2(-4 + 4i + x) + x(-4 + 4i + x))(-4 + -4i + x) = 0 ((-4 * 2 + 4i * 2 + x * 2) + x(-4 + 4i + x))(-4 + -4i + x) = 0 ((-8 + 8i + 2x) + x(-4 + 4i + x))(-4 + -4i + x) = 0 (-8 + 8i + 2x + (-4 * x + 4i * x + x * x))(-4 + -4i + x) = 0 Reorder the terms: (-8 + 8i + 2x + (4ix + -4x + x2))(-4 + -4i + x) = 0 (-8 + 8i + 2x + (4ix + -4x + x2))(-4 + -4i + x) = 0 Reorder the terms: (-8 + 8i + 4ix + 2x + -4x + x2)(-4 + -4i + x) = 0 Combine like terms: 2x + -4x = -2x (-8 + 8i + 4ix + -2x + x2)(-4 + -4i + x) = 0 Multiply (-8 + 8i + 4ix + -2x + x2) * (-4 + -4i + x) (-8(-4 + -4i + x) + 8i * (-4 + -4i + x) + 4ix * (-4 + -4i + x) + -2x * (-4 + -4i + x) + x2(-4 + -4i + x)) = 0 ((-4 * -8 + -4i * -8 + x * -8) + 8i * (-4 + -4i + x) + 4ix * (-4 + -4i + x) + -2x * (-4 + -4i + x) + x2(-4 + -4i + x)) = 0 ((32 + 32i + -8x) + 8i * (-4 + -4i + x) + 4ix * (-4 + -4i + x) + -2x * (-4 + -4i + x) + x2(-4 + -4i + x)) = 0 (32 + 32i + -8x + (-4 * 8i + -4i * 8i + x * 8i) + 4ix * (-4 + -4i + x) + -2x * (-4 + -4i + x) + x2(-4 + -4i + x)) = 0 Reorder the terms: (32 + 32i + -8x + (-32i + 8ix + -32i2) + 4ix * (-4 + -4i + x) + -2x * (-4 + -4i + x) + x2(-4 + -4i + x)) = 0 (32 + 32i + -8x + (-32i + 8ix + -32i2) + 4ix * (-4 + -4i + x) + -2x * (-4 + -4i + x) + x2(-4 + -4i + x)) = 0 (32 + 32i + -8x + -32i + 8ix + -32i2 + (-4 * 4ix + -4i * 4ix + x * 4ix) + -2x * (-4 + -4i + x) + x2(-4 + -4i + x)) = 0 Reorder the terms: (32 + 32i + -8x + -32i + 8ix + -32i2 + (-16ix + 4ix2 + -16i2x) + -2x * (-4 + -4i + x) + x2(-4 + -4i + x)) = 0 (32 + 32i + -8x + -32i + 8ix + -32i2 + (-16ix + 4ix2 + -16i2x) + -2x * (-4 + -4i + x) + x2(-4 + -4i + x)) = 0 (32 + 32i + -8x + -32i + 8ix + -32i2 + -16ix + 4ix2 + -16i2x + (-4 * -2x + -4i * -2x + x * -2x) + x2(-4 + -4i + x)) = 0 Reorder the terms: (32 + 32i + -8x + -32i + 8ix + -32i2 + -16ix + 4ix2 + -16i2x + (8ix + 8x + -2x2) + x2(-4 + -4i + x)) = 0 (32 + 32i + -8x + -32i + 8ix + -32i2 + -16ix + 4ix2 + -16i2x + (8ix + 8x + -2x2) + x2(-4 + -4i + x)) = 0 (32 + 32i + -8x + -32i + 8ix + -32i2 + -16ix + 4ix2 + -16i2x + 8ix + 8x + -2x2 + (-4 * x2 + -4i * x2 + x * x2)) = 0 Reorder the terms: (32 + 32i + -8x + -32i + 8ix + -32i2 + -16ix + 4ix2 + -16i2x + 8ix + 8x + -2x2 + (-4ix2 + -4x2 + x3)) = 0 (32 + 32i + -8x + -32i + 8ix + -32i2 + -16ix + 4ix2 + -16i2x + 8ix + 8x + -2x2 + (-4ix2 + -4x2 + x3)) = 0 Reorder the terms: (32 + 32i + -32i + 8ix + -16ix + 8ix + 4ix2 + -4ix2 + -32i2 + -16i2x + -8x + 8x + -2x2 + -4x2 + x3) = 0 Combine like terms: 32i + -32i = 0 (32 + 0 + 8ix + -16ix + 8ix + 4ix2 + -4ix2 + -32i2 + -16i2x + -8x + 8x + -2x2 + -4x2 + x3) = 0 (32 + 8ix + -16ix + 8ix + 4ix2 + -4ix2 + -32i2 + -16i2x + -8x + 8x + -2x2 + -4x2 + x3) = 0 Combine like terms: 8ix + -16ix = -8ix (32 + -8ix + 8ix + 4ix2 + -4ix2 + -32i2 + -16i2x + -8x + 8x + -2x2 + -4x2 + x3) = 0 Combine like terms: -8ix + 8ix = 0 (32 + 0 + 4ix2 + -4ix2 + -32i2 + -16i2x + -8x + 8x + -2x2 + -4x2 + x3) = 0 (32 + 4ix2 + -4ix2 + -32i2 + -16i2x + -8x + 8x + -2x2 + -4x2 + x3) = 0 Combine like terms: 4ix2 + -4ix2 = 0 (32 + 0 + -32i2 + -16i2x + -8x + 8x + -2x2 + -4x2 + x3) = 0 (32 + -32i2 + -16i2x + -8x + 8x + -2x2 + -4x2 + x3) = 0 Combine like terms: -8x + 8x = 0 (32 + -32i2 + -16i2x + 0 + -2x2 + -4x2 + x3) = 0 (32 + -32i2 + -16i2x + -2x2 + -4x2 + x3) = 0 Combine like terms: -2x2 + -4x2 = -6x2 (32 + -32i2 + -16i2x + -6x2 + x3) = 0 Solving 32 + -32i2 + -16i2x + -6x2 + x3 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-32' to each side of the equation. 32 + -32i2 + -16i2x + -6x2 + -32 + x3 = 0 + -32 Reorder the terms: 32 + -32 + -32i2 + -16i2x + -6x2 + x3 = 0 + -32 Combine like terms: 32 + -32 = 0 0 + -32i2 + -16i2x + -6x2 + x3 = 0 + -32 -32i2 + -16i2x + -6x2 + x3 = 0 + -32 Combine like terms: 0 + -32 = -32 -32i2 + -16i2x + -6x2 + x3 = -32 Add '6x2' to each side of the equation. -32i2 + -16i2x + -6x2 + 6x2 + x3 = -32 + 6x2 Combine like terms: -6x2 + 6x2 = 0 -32i2 + -16i2x + 0 + x3 = -32 + 6x2 -32i2 + -16i2x + x3 = -32 + 6x2 Add '-1x3' to each side of the equation. -32i2 + -16i2x + x3 + -1x3 = -32 + 6x2 + -1x3 Combine like terms: x3 + -1x3 = 0 -32i2 + -16i2x + 0 = -32 + 6x2 + -1x3 -32i2 + -16i2x = -32 + 6x2 + -1x3 Reorder the terms: 32 + -32i2 + -16i2x + -6x2 + x3 = -32 + 6x2 + -1x3 + 32 + -6x2 + x3 Reorder the terms: 32 + -32i2 + -16i2x + -6x2 + x3 = -32 + 32 + 6x2 + -6x2 + -1x3 + x3 Combine like terms: -32 + 32 = 0 32 + -32i2 + -16i2x + -6x2 + x3 = 0 + 6x2 + -6x2 + -1x3 + x3 32 + -32i2 + -16i2x + -6x2 + x3 = 6x2 + -6x2 + -1x3 + x3 Combine like terms: 6x2 + -6x2 = 0 32 + -32i2 + -16i2x + -6x2 + x3 = 0 + -1x3 + x3 32 + -32i2 + -16i2x + -6x2 + x3 = -1x3 + x3 Combine like terms: -1x3 + x3 = 0 32 + -32i2 + -16i2x + -6x2 + x3 = 0 The solution to this equation could not be determined.
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