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Simplifying (x + 5)(x + 5)(3i + x + 4)(-3i + x + 4) = 0 Reorder the terms: (5 + x)(x + 5)(3i + x + 4)(-3i + x + 4) = 0 Reorder the terms: (5 + x)(5 + x)(3i + x + 4)(-3i + x + 4) = 0 Reorder the terms: (5 + x)(5 + x)(4 + 3i + x)(-3i + x + 4) = 0 Reorder the terms: (5 + x)(5 + x)(4 + 3i + x)(4 + -3i + x) = 0 Multiply (5 + x) * (5 + x) (5(5 + x) + x(5 + x))(4 + 3i + x)(4 + -3i + x) = 0 ((5 * 5 + x * 5) + x(5 + x))(4 + 3i + x)(4 + -3i + x) = 0 ((25 + 5x) + x(5 + x))(4 + 3i + x)(4 + -3i + x) = 0 (25 + 5x + (5 * x + x * x))(4 + 3i + x)(4 + -3i + x) = 0 (25 + 5x + (5x + x2))(4 + 3i + x)(4 + -3i + x) = 0 Combine like terms: 5x + 5x = 10x (25 + 10x + x2)(4 + 3i + x)(4 + -3i + x) = 0 Multiply (25 + 10x + x2) * (4 + 3i + x) (25(4 + 3i + x) + 10x * (4 + 3i + x) + x2(4 + 3i + x))(4 + -3i + x) = 0 ((4 * 25 + 3i * 25 + x * 25) + 10x * (4 + 3i + x) + x2(4 + 3i + x))(4 + -3i + x) = 0 ((100 + 75i + 25x) + 10x * (4 + 3i + x) + x2(4 + 3i + x))(4 + -3i + x) = 0 (100 + 75i + 25x + (4 * 10x + 3i * 10x + x * 10x) + x2(4 + 3i + x))(4 + -3i + x) = 0 Reorder the terms: (100 + 75i + 25x + (30ix + 40x + 10x2) + x2(4 + 3i + x))(4 + -3i + x) = 0 (100 + 75i + 25x + (30ix + 40x + 10x2) + x2(4 + 3i + x))(4 + -3i + x) = 0 (100 + 75i + 25x + 30ix + 40x + 10x2 + (4 * x2 + 3i * x2 + x * x2))(4 + -3i + x) = 0 Reorder the terms: (100 + 75i + 25x + 30ix + 40x + 10x2 + (3ix2 + 4x2 + x3))(4 + -3i + x) = 0 (100 + 75i + 25x + 30ix + 40x + 10x2 + (3ix2 + 4x2 + x3))(4 + -3i + x) = 0 Reorder the terms: (100 + 75i + 30ix + 3ix2 + 25x + 40x + 10x2 + 4x2 + x3)(4 + -3i + x) = 0 Combine like terms: 25x + 40x = 65x (100 + 75i + 30ix + 3ix2 + 65x + 10x2 + 4x2 + x3)(4 + -3i + x) = 0 Combine like terms: 10x2 + 4x2 = 14x2 (100 + 75i + 30ix + 3ix2 + 65x + 14x2 + x3)(4 + -3i + x) = 0 Multiply (100 + 75i + 30ix + 3ix2 + 65x + 14x2 + x3) * (4 + -3i + x) (100(4 + -3i + x) + 75i * (4 + -3i + x) + 30ix * (4 + -3i + x) + 3ix2 * (4 + -3i + x) + 65x * (4 + -3i + x) + 14x2 * (4 + -3i + x) + x3(4 + -3i + x)) = 0 ((4 * 100 + -3i * 100 + x * 100) + 75i * (4 + -3i + x) + 30ix * (4 + -3i + x) + 3ix2 * (4 + -3i + x) + 65x * (4 + -3i + x) + 14x2 * (4 + -3i + x) + x3(4 + -3i + x)) = 0 ((400 + -300i + 100x) + 75i * (4 + -3i + x) + 30ix * (4 + -3i + x) + 3ix2 * (4 + -3i + x) + 65x * (4 + -3i + x) + 14x2 * (4 + -3i + x) + x3(4 + -3i + x)) = 0 (400 + -300i + 100x + (4 * 75i + -3i * 75i + x * 75i) + 30ix * (4 + -3i + x) + 3ix2 * (4 + -3i + x) + 65x * (4 + -3i + x) + 14x2 * (4 + -3i + x) + x3(4 + -3i + x)) = 0 Reorder the terms: (400 + -300i + 100x + (300i + 75ix + -225i2) + 30ix * (4 + -3i + x) + 3ix2 * (4 + -3i + x) + 65x * (4 + -3i + x) + 14x2 * (4 + -3i + x) + x3(4 + -3i + x)) = 0 (400 + -300i + 100x + (300i + 75ix + -225i2) + 30ix * (4 + -3i + x) + 3ix2 * (4 + -3i + x) + 65x * (4 + -3i + x) + 14x2 * (4 + -3i + x) + x3(4 + -3i + x)) = 0 (400 + -300i + 100x + 300i + 75ix + -225i2 + (4 * 30ix + -3i * 30ix + x * 30ix) + 3ix2 * (4 + -3i + x) + 65x * (4 + -3i + x) + 14x2 * (4 + -3i + x) + x3(4 + -3i + x)) = 0 Reorder the terms: (400 + -300i + 100x + 300i + 75ix + -225i2 + (120ix + 30ix2 + -90i2x) + 3ix2 * (4 + -3i + x) + 65x * (4 + -3i + x) + 14x2 * (4 + -3i + x) + x3(4 + -3i + x)) = 0 (400 + -300i + 100x + 300i + 75ix + -225i2 + (120ix + 30ix2 + -90i2x) + 3ix2 * (4 + -3i + x) + 65x * (4 + -3i + x) + 14x2 * (4 + -3i + x) + x3(4 + -3i + x)) = 0 (400 + -300i + 100x + 300i + 75ix + -225i2 + 120ix + 30ix2 + -90i2x + (4 * 3ix2 + -3i * 3ix2 + x * 3ix2) + 65x * (4 + -3i + x) + 14x2 * (4 + -3i + x) + x3(4 + -3i + x)) = 0 Reorder the terms: (400 + -300i + 100x + 300i + 75ix + -225i2 + 120ix + 30ix2 + -90i2x + (12ix2 + 3ix3 + -9i2x2) + 65x * (4 + -3i + x) + 14x2 * (4 + -3i + x) + x3(4 + -3i + x)) = 0 (400 + -300i + 100x + 300i + 75ix + -225i2 + 120ix + 30ix2 + -90i2x + (12ix2 + 3ix3 + -9i2x2) + 65x * (4 + -3i + x) + 14x2 * (4 + -3i + x) + x3(4 + -3i + x)) = 0 (400 + -300i + 100x + 300i + 75ix + -225i2 + 120ix + 30ix2 + -90i2x + 12ix2 + 3ix3 + -9i2x2 + (4 * 65x + -3i * 65x + x * 65x) + 14x2 * (4 + -3i + x) + x3(4 + -3i + x)) = 0 Reorder the terms: (400 + -300i + 100x + 300i + 75ix + -225i2 + 120ix + 30ix2 + -90i2x + 12ix2 + 3ix3 + -9i2x2 + (-195ix + 260x + 65x2) + 14x2 * (4 + -3i + x) + x3(4 + -3i + x)) = 0 (400 + -300i + 100x + 300i + 75ix + -225i2 + 120ix + 30ix2 + -90i2x + 12ix2 + 3ix3 + -9i2x2 + (-195ix + 260x + 65x2) + 14x2 * (4 + -3i + x) + x3(4 + -3i + x)) = 0 (400 + -300i + 100x + 300i + 75ix + -225i2 + 120ix + 30ix2 + -90i2x + 12ix2 + 3ix3 + -9i2x2 + -195ix + 260x + 65x2 + (4 * 14x2 + -3i * 14x2 + x * 14x2) + x3(4 + -3i + x)) = 0 Reorder the terms: (400 + -300i + 100x + 300i + 75ix + -225i2 + 120ix + 30ix2 + -90i2x + 12ix2 + 3ix3 + -9i2x2 + -195ix + 260x + 65x2 + (-42ix2 + 56x2 + 14x3) + x3(4 + -3i + x)) = 0 (400 + -300i + 100x + 300i + 75ix + -225i2 + 120ix + 30ix2 + -90i2x + 12ix2 + 3ix3 + -9i2x2 + -195ix + 260x + 65x2 + (-42ix2 + 56x2 + 14x3) + x3(4 + -3i + x)) = 0 (400 + -300i + 100x + 300i + 75ix + -225i2 + 120ix + 30ix2 + -90i2x + 12ix2 + 3ix3 + -9i2x2 + -195ix + 260x + 65x2 + -42ix2 + 56x2 + 14x3 + (4 * x3 + -3i * x3 + x * x3)) = 0 Reorder the terms: (400 + -300i + 100x + 300i + 75ix + -225i2 + 120ix + 30ix2 + -90i2x + 12ix2 + 3ix3 + -9i2x2 + -195ix + 260x + 65x2 + -42ix2 + 56x2 + 14x3 + (-3ix3 + 4x3 + x4)) = 0 (400 + -300i + 100x + 300i + 75ix + -225i2 + 120ix + 30ix2 + -90i2x + 12ix2 + 3ix3 + -9i2x2 + -195ix + 260x + 65x2 + -42ix2 + 56x2 + 14x3 + (-3ix3 + 4x3 + x4)) = 0 Reorder the terms: (400 + -300i + 300i + 75ix + 120ix + -195ix + 30ix2 + 12ix2 + -42ix2 + 3ix3 + -3ix3 + -225i2 + -90i2x + -9i2x2 + 100x + 260x + 65x2 + 56x2 + 14x3 + 4x3 + x4) = 0 Combine like terms: -300i + 300i = 0 (400 + 0 + 75ix + 120ix + -195ix + 30ix2 + 12ix2 + -42ix2 + 3ix3 + -3ix3 + -225i2 + -90i2x + -9i2x2 + 100x + 260x + 65x2 + 56x2 + 14x3 + 4x3 + x4) = 0 (400 + 75ix + 120ix + -195ix + 30ix2 + 12ix2 + -42ix2 + 3ix3 + -3ix3 + -225i2 + -90i2x + -9i2x2 + 100x + 260x + 65x2 + 56x2 + 14x3 + 4x3 + x4) = 0 Combine like terms: 75ix + 120ix = 195ix (400 + 195ix + -195ix + 30ix2 + 12ix2 + -42ix2 + 3ix3 + -3ix3 + -225i2 + -90i2x + -9i2x2 + 100x + 260x + 65x2 + 56x2 + 14x3 + 4x3 + x4) = 0 Combine like terms: 195ix + -195ix = 0 (400 + 0 + 30ix2 + 12ix2 + -42ix2 + 3ix3 + -3ix3 + -225i2 + -90i2x + -9i2x2 + 100x + 260x + 65x2 + 56x2 + 14x3 + 4x3 + x4) = 0 (400 + 30ix2 + 12ix2 + -42ix2 + 3ix3 + -3ix3 + -225i2 + -90i2x + -9i2x2 + 100x + 260x + 65x2 + 56x2 + 14x3 + 4x3 + x4) = 0 Combine like terms: 30ix2 + 12ix2 = 42ix2 (400 + 42ix2 + -42ix2 + 3ix3 + -3ix3 + -225i2 + -90i2x + -9i2x2 + 100x + 260x + 65x2 + 56x2 + 14x3 + 4x3 + x4) = 0 Combine like terms: 42ix2 + -42ix2 = 0 (400 + 0 + 3ix3 + -3ix3 + -225i2 + -90i2x + -9i2x2 + 100x + 260x + 65x2 + 56x2 + 14x3 + 4x3 + x4) = 0 (400 + 3ix3 + -3ix3 + -225i2 + -90i2x + -9i2x2 + 100x + 260x + 65x2 + 56x2 + 14x3 + 4x3 + x4) = 0 Combine like terms: 3ix3 + -3ix3 = 0 (400 + 0 + -225i2 + -90i2x + -9i2x2 + 100x + 260x + 65x2 + 56x2 + 14x3 + 4x3 + x4) = 0 (400 + -225i2 + -90i2x + -9i2x2 + 100x + 260x + 65x2 + 56x2 + 14x3 + 4x3 + x4) = 0 Combine like terms: 100x + 260x = 360x (400 + -225i2 + -90i2x + -9i2x2 + 360x + 65x2 + 56x2 + 14x3 + 4x3 + x4) = 0 Combine like terms: 65x2 + 56x2 = 121x2 (400 + -225i2 + -90i2x + -9i2x2 + 360x + 121x2 + 14x3 + 4x3 + x4) = 0 Combine like terms: 14x3 + 4x3 = 18x3 (400 + -225i2 + -90i2x + -9i2x2 + 360x + 121x2 + 18x3 + x4) = 0 Solving 400 + -225i2 + -90i2x + -9i2x2 + 360x + 121x2 + 18x3 + x4 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-400' to each side of the equation. 400 + -225i2 + -90i2x + -9i2x2 + 360x + 121x2 + 18x3 + -400 + x4 = 0 + -400 Reorder the terms: 400 + -400 + -225i2 + -90i2x + -9i2x2 + 360x + 121x2 + 18x3 + x4 = 0 + -400 Combine like terms: 400 + -400 = 0 0 + -225i2 + -90i2x + -9i2x2 + 360x + 121x2 + 18x3 + x4 = 0 + -400 -225i2 + -90i2x + -9i2x2 + 360x + 121x2 + 18x3 + x4 = 0 + -400 Combine like terms: 0 + -400 = -400 -225i2 + -90i2x + -9i2x2 + 360x + 121x2 + 18x3 + x4 = -400 Add '-360x' to each side of the equation. -225i2 + -90i2x + -9i2x2 + 360x + 121x2 + 18x3 + -360x + x4 = -400 + -360x Reorder the terms: -225i2 + -90i2x + -9i2x2 + 360x + -360x + 121x2 + 18x3 + x4 = -400 + -360x Combine like terms: 360x + -360x = 0 -225i2 + -90i2x + -9i2x2 + 0 + 121x2 + 18x3 + x4 = -400 + -360x -225i2 + -90i2x + -9i2x2 + 121x2 + 18x3 + x4 = -400 + -360x Add '-121x2' to each side of the equation. -225i2 + -90i2x + -9i2x2 + 121x2 + 18x3 + -121x2 + x4 = -400 + -360x + -121x2 Reorder the terms: -225i2 + -90i2x + -9i2x2 + 121x2 + -121x2 + 18x3 + x4 = -400 + -360x + -121x2 Combine like terms: 121x2 + -121x2 = 0 -225i2 + -90i2x + -9i2x2 + 0 + 18x3 + x4 = -400 + -360x + -121x2 -225i2 + -90i2x + -9i2x2 + 18x3 + x4 = -400 + -360x + -121x2 Add '-18x3' to each side of the equation. -225i2 + -90i2x + -9i2x2 + 18x3 + -18x3 + x4 = -400 + -360x + -121x2 + -18x3 Combine like terms: 18x3 + -18x3 = 0 -225i2 + -90i2x + -9i2x2 + 0 + x4 = -400 + -360x + -121x2 + -18x3 -225i2 + -90i2x + -9i2x2 + x4 = -400 + -360x + -121x2 + -18x3 Add '-1x4' to each side of the equation. -225i2 + -90i2x + -9i2x2 + x4 + -1x4 = -400 + -360x + -121x2 + -18x3 + -1x4 Combine like terms: x4 + -1x4 = 0 -225i2 + -90i2x + -9i2x2 + 0 = -400 + -360x + -121x2 + -18x3 + -1x4 -225i2 + -90i2x + -9i2x2 = -400 + -360x + -121x2 + -18x3 + -1x4 Reorder the terms: 400 + -225i2 + -90i2x + -9i2x2 + 360x + 121x2 + 18x3 + x4 = -400 + -360x + -121x2 + -18x3 + -1x4 + 400 + 360x + 121x2 + 18x3 + x4 Reorder the terms: 400 + -225i2 + -90i2x + -9i2x2 + 360x + 121x2 + 18x3 + x4 = -400 + 400 + -360x + 360x + -121x2 + 121x2 + -18x3 + 18x3 + -1x4 + x4 Combine like terms: -400 + 400 = 0 400 + -225i2 + -90i2x + -9i2x2 + 360x + 121x2 + 18x3 + x4 = 0 + -360x + 360x + -121x2 + 121x2 + -18x3 + 18x3 + -1x4 + x4 400 + -225i2 + -90i2x + -9i2x2 + 360x + 121x2 + 18x3 + x4 = -360x + 360x + -121x2 + 121x2 + -18x3 + 18x3 + -1x4 + x4 Combine like terms: -360x + 360x = 0 400 + -225i2 + -90i2x + -9i2x2 + 360x + 121x2 + 18x3 + x4 = 0 + -121x2 + 121x2 + -18x3 + 18x3 + -1x4 + x4 400 + -225i2 + -90i2x + -9i2x2 + 360x + 121x2 + 18x3 + x4 = -121x2 + 121x2 + -18x3 + 18x3 + -1x4 + x4 Combine like terms: -121x2 + 121x2 = 0 400 + -225i2 + -90i2x + -9i2x2 + 360x + 121x2 + 18x3 + x4 = 0 + -18x3 + 18x3 + -1x4 + x4 400 + -225i2 + -90i2x + -9i2x2 + 360x + 121x2 + 18x3 + x4 = -18x3 + 18x3 + -1x4 + x4 Combine like terms: -18x3 + 18x3 = 0 400 + -225i2 + -90i2x + -9i2x2 + 360x + 121x2 + 18x3 + x4 = 0 + -1x4 + x4 400 + -225i2 + -90i2x + -9i2x2 + 360x + 121x2 + 18x3 + x4 = -1x4 + x4 Combine like terms: -1x4 + x4 = 0 400 + -225i2 + -90i2x + -9i2x2 + 360x + 121x2 + 18x3 + x4 = 0 The solution to this equation could not be determined.
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