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