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Simplifying (x + -4)(x + 8)(x + -2 + -5i)(x + -2 + 5i) = 0 Reorder the terms: (-4 + x)(x + 8)(x + -2 + -5i)(x + -2 + 5i) = 0 Reorder the terms: (-4 + x)(8 + x)(x + -2 + -5i)(x + -2 + 5i) = 0 Reorder the terms: (-4 + x)(8 + x)(-2 + -5i + x)(x + -2 + 5i) = 0 Reorder the terms: (-4 + x)(8 + x)(-2 + -5i + x)(-2 + 5i + x) = 0 Multiply (-4 + x) * (8 + x) (-4(8 + x) + x(8 + x))(-2 + -5i + x)(-2 + 5i + x) = 0 ((8 * -4 + x * -4) + x(8 + x))(-2 + -5i + x)(-2 + 5i + x) = 0 ((-32 + -4x) + x(8 + x))(-2 + -5i + x)(-2 + 5i + x) = 0 (-32 + -4x + (8 * x + x * x))(-2 + -5i + x)(-2 + 5i + x) = 0 (-32 + -4x + (8x + x2))(-2 + -5i + x)(-2 + 5i + x) = 0 Combine like terms: -4x + 8x = 4x (-32 + 4x + x2)(-2 + -5i + x)(-2 + 5i + x) = 0 Multiply (-32 + 4x + x2) * (-2 + -5i + x) (-32(-2 + -5i + x) + 4x * (-2 + -5i + x) + x2(-2 + -5i + x))(-2 + 5i + x) = 0 ((-2 * -32 + -5i * -32 + x * -32) + 4x * (-2 + -5i + x) + x2(-2 + -5i + x))(-2 + 5i + x) = 0 ((64 + 160i + -32x) + 4x * (-2 + -5i + x) + x2(-2 + -5i + x))(-2 + 5i + x) = 0 (64 + 160i + -32x + (-2 * 4x + -5i * 4x + x * 4x) + x2(-2 + -5i + x))(-2 + 5i + x) = 0 Reorder the terms: (64 + 160i + -32x + (-20ix + -8x + 4x2) + x2(-2 + -5i + x))(-2 + 5i + x) = 0 (64 + 160i + -32x + (-20ix + -8x + 4x2) + x2(-2 + -5i + x))(-2 + 5i + x) = 0 (64 + 160i + -32x + -20ix + -8x + 4x2 + (-2 * x2 + -5i * x2 + x * x2))(-2 + 5i + x) = 0 Reorder the terms: (64 + 160i + -32x + -20ix + -8x + 4x2 + (-5ix2 + -2x2 + x3))(-2 + 5i + x) = 0 (64 + 160i + -32x + -20ix + -8x + 4x2 + (-5ix2 + -2x2 + x3))(-2 + 5i + x) = 0 Reorder the terms: (64 + 160i + -20ix + -5ix2 + -32x + -8x + 4x2 + -2x2 + x3)(-2 + 5i + x) = 0 Combine like terms: -32x + -8x = -40x (64 + 160i + -20ix + -5ix2 + -40x + 4x2 + -2x2 + x3)(-2 + 5i + x) = 0 Combine like terms: 4x2 + -2x2 = 2x2 (64 + 160i + -20ix + -5ix2 + -40x + 2x2 + x3)(-2 + 5i + x) = 0 Multiply (64 + 160i + -20ix + -5ix2 + -40x + 2x2 + x3) * (-2 + 5i + x) (64(-2 + 5i + x) + 160i * (-2 + 5i + x) + -20ix * (-2 + 5i + x) + -5ix2 * (-2 + 5i + x) + -40x * (-2 + 5i + x) + 2x2 * (-2 + 5i + x) + x3(-2 + 5i + x)) = 0 ((-2 * 64 + 5i * 64 + x * 64) + 160i * (-2 + 5i + x) + -20ix * (-2 + 5i + x) + -5ix2 * (-2 + 5i + x) + -40x * (-2 + 5i + x) + 2x2 * (-2 + 5i + x) + x3(-2 + 5i + x)) = 0 ((-128 + 320i + 64x) + 160i * (-2 + 5i + x) + -20ix * (-2 + 5i + x) + -5ix2 * (-2 + 5i + x) + -40x * (-2 + 5i + x) + 2x2 * (-2 + 5i + x) + x3(-2 + 5i + x)) = 0 (-128 + 320i + 64x + (-2 * 160i + 5i * 160i + x * 160i) + -20ix * (-2 + 5i + x) + -5ix2 * (-2 + 5i + x) + -40x * (-2 + 5i + x) + 2x2 * (-2 + 5i + x) + x3(-2 + 5i + x)) = 0 Reorder the terms: (-128 + 320i + 64x + (-320i + 160ix + 800i2) + -20ix * (-2 + 5i + x) + -5ix2 * (-2 + 5i + x) + -40x * (-2 + 5i + x) + 2x2 * (-2 + 5i + x) + x3(-2 + 5i + x)) = 0 (-128 + 320i + 64x + (-320i + 160ix + 800i2) + -20ix * (-2 + 5i + x) + -5ix2 * (-2 + 5i + x) + -40x * (-2 + 5i + x) + 2x2 * (-2 + 5i + x) + x3(-2 + 5i + x)) = 0 (-128 + 320i + 64x + -320i + 160ix + 800i2 + (-2 * -20ix + 5i * -20ix + x * -20ix) + -5ix2 * (-2 + 5i + x) + -40x * (-2 + 5i + x) + 2x2 * (-2 + 5i + x) + x3(-2 + 5i + x)) = 0 Reorder the terms: (-128 + 320i + 64x + -320i + 160ix + 800i2 + (40ix + -20ix2 + -100i2x) + -5ix2 * (-2 + 5i + x) + -40x * (-2 + 5i + x) + 2x2 * (-2 + 5i + x) + x3(-2 + 5i + x)) = 0 (-128 + 320i + 64x + -320i + 160ix + 800i2 + (40ix + -20ix2 + -100i2x) + -5ix2 * (-2 + 5i + x) + -40x * (-2 + 5i + x) + 2x2 * (-2 + 5i + x) + x3(-2 + 5i + x)) = 0 (-128 + 320i + 64x + -320i + 160ix + 800i2 + 40ix + -20ix2 + -100i2x + (-2 * -5ix2 + 5i * -5ix2 + x * -5ix2) + -40x * (-2 + 5i + x) + 2x2 * (-2 + 5i + x) + x3(-2 + 5i + x)) = 0 Reorder the terms: (-128 + 320i + 64x + -320i + 160ix + 800i2 + 40ix + -20ix2 + -100i2x + (10ix2 + -5ix3 + -25i2x2) + -40x * (-2 + 5i + x) + 2x2 * (-2 + 5i + x) + x3(-2 + 5i + x)) = 0 (-128 + 320i + 64x + -320i + 160ix + 800i2 + 40ix + -20ix2 + -100i2x + (10ix2 + -5ix3 + -25i2x2) + -40x * (-2 + 5i + x) + 2x2 * (-2 + 5i + x) + x3(-2 + 5i + x)) = 0 (-128 + 320i + 64x + -320i + 160ix + 800i2 + 40ix + -20ix2 + -100i2x + 10ix2 + -5ix3 + -25i2x2 + (-2 * -40x + 5i * -40x + x * -40x) + 2x2 * (-2 + 5i + x) + x3(-2 + 5i + x)) = 0 Reorder the terms: (-128 + 320i + 64x + -320i + 160ix + 800i2 + 40ix + -20ix2 + -100i2x + 10ix2 + -5ix3 + -25i2x2 + (-200ix + 80x + -40x2) + 2x2 * (-2 + 5i + x) + x3(-2 + 5i + x)) = 0 (-128 + 320i + 64x + -320i + 160ix + 800i2 + 40ix + -20ix2 + -100i2x + 10ix2 + -5ix3 + -25i2x2 + (-200ix + 80x + -40x2) + 2x2 * (-2 + 5i + x) + x3(-2 + 5i + x)) = 0 (-128 + 320i + 64x + -320i + 160ix + 800i2 + 40ix + -20ix2 + -100i2x + 10ix2 + -5ix3 + -25i2x2 + -200ix + 80x + -40x2 + (-2 * 2x2 + 5i * 2x2 + x * 2x2) + x3(-2 + 5i + x)) = 0 Reorder the terms: (-128 + 320i + 64x + -320i + 160ix + 800i2 + 40ix + -20ix2 + -100i2x + 10ix2 + -5ix3 + -25i2x2 + -200ix + 80x + -40x2 + (10ix2 + -4x2 + 2x3) + x3(-2 + 5i + x)) = 0 (-128 + 320i + 64x + -320i + 160ix + 800i2 + 40ix + -20ix2 + -100i2x + 10ix2 + -5ix3 + -25i2x2 + -200ix + 80x + -40x2 + (10ix2 + -4x2 + 2x3) + x3(-2 + 5i + x)) = 0 (-128 + 320i + 64x + -320i + 160ix + 800i2 + 40ix + -20ix2 + -100i2x + 10ix2 + -5ix3 + -25i2x2 + -200ix + 80x + -40x2 + 10ix2 + -4x2 + 2x3 + (-2 * x3 + 5i * x3 + x * x3)) = 0 Reorder the terms: (-128 + 320i + 64x + -320i + 160ix + 800i2 + 40ix + -20ix2 + -100i2x + 10ix2 + -5ix3 + -25i2x2 + -200ix + 80x + -40x2 + 10ix2 + -4x2 + 2x3 + (5ix3 + -2x3 + x4)) = 0 (-128 + 320i + 64x + -320i + 160ix + 800i2 + 40ix + -20ix2 + -100i2x + 10ix2 + -5ix3 + -25i2x2 + -200ix + 80x + -40x2 + 10ix2 + -4x2 + 2x3 + (5ix3 + -2x3 + x4)) = 0 Reorder the terms: (-128 + 320i + -320i + 160ix + 40ix + -200ix + -20ix2 + 10ix2 + 10ix2 + -5ix3 + 5ix3 + 800i2 + -100i2x + -25i2x2 + 64x + 80x + -40x2 + -4x2 + 2x3 + -2x3 + x4) = 0 Combine like terms: 320i + -320i = 0 (-128 + 0 + 160ix + 40ix + -200ix + -20ix2 + 10ix2 + 10ix2 + -5ix3 + 5ix3 + 800i2 + -100i2x + -25i2x2 + 64x + 80x + -40x2 + -4x2 + 2x3 + -2x3 + x4) = 0 (-128 + 160ix + 40ix + -200ix + -20ix2 + 10ix2 + 10ix2 + -5ix3 + 5ix3 + 800i2 + -100i2x + -25i2x2 + 64x + 80x + -40x2 + -4x2 + 2x3 + -2x3 + x4) = 0 Combine like terms: 160ix + 40ix = 200ix (-128 + 200ix + -200ix + -20ix2 + 10ix2 + 10ix2 + -5ix3 + 5ix3 + 800i2 + -100i2x + -25i2x2 + 64x + 80x + -40x2 + -4x2 + 2x3 + -2x3 + x4) = 0 Combine like terms: 200ix + -200ix = 0 (-128 + 0 + -20ix2 + 10ix2 + 10ix2 + -5ix3 + 5ix3 + 800i2 + -100i2x + -25i2x2 + 64x + 80x + -40x2 + -4x2 + 2x3 + -2x3 + x4) = 0 (-128 + -20ix2 + 10ix2 + 10ix2 + -5ix3 + 5ix3 + 800i2 + -100i2x + -25i2x2 + 64x + 80x + -40x2 + -4x2 + 2x3 + -2x3 + x4) = 0 Combine like terms: -20ix2 + 10ix2 = -10ix2 (-128 + -10ix2 + 10ix2 + -5ix3 + 5ix3 + 800i2 + -100i2x + -25i2x2 + 64x + 80x + -40x2 + -4x2 + 2x3 + -2x3 + x4) = 0 Combine like terms: -10ix2 + 10ix2 = 0 (-128 + 0 + -5ix3 + 5ix3 + 800i2 + -100i2x + -25i2x2 + 64x + 80x + -40x2 + -4x2 + 2x3 + -2x3 + x4) = 0 (-128 + -5ix3 + 5ix3 + 800i2 + -100i2x + -25i2x2 + 64x + 80x + -40x2 + -4x2 + 2x3 + -2x3 + x4) = 0 Combine like terms: -5ix3 + 5ix3 = 0 (-128 + 0 + 800i2 + -100i2x + -25i2x2 + 64x + 80x + -40x2 + -4x2 + 2x3 + -2x3 + x4) = 0 (-128 + 800i2 + -100i2x + -25i2x2 + 64x + 80x + -40x2 + -4x2 + 2x3 + -2x3 + x4) = 0 Combine like terms: 64x + 80x = 144x (-128 + 800i2 + -100i2x + -25i2x2 + 144x + -40x2 + -4x2 + 2x3 + -2x3 + x4) = 0 Combine like terms: -40x2 + -4x2 = -44x2 (-128 + 800i2 + -100i2x + -25i2x2 + 144x + -44x2 + 2x3 + -2x3 + x4) = 0 Combine like terms: 2x3 + -2x3 = 0 (-128 + 800i2 + -100i2x + -25i2x2 + 144x + -44x2 + 0 + x4) = 0 (-128 + 800i2 + -100i2x + -25i2x2 + 144x + -44x2 + x4) = 0 Solving -128 + 800i2 + -100i2x + -25i2x2 + 144x + -44x2 + x4 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '128' to each side of the equation. -128 + 800i2 + -100i2x + -25i2x2 + 144x + -44x2 + 128 + x4 = 0 + 128 Reorder the terms: -128 + 128 + 800i2 + -100i2x + -25i2x2 + 144x + -44x2 + x4 = 0 + 128 Combine like terms: -128 + 128 = 0 0 + 800i2 + -100i2x + -25i2x2 + 144x + -44x2 + x4 = 0 + 128 800i2 + -100i2x + -25i2x2 + 144x + -44x2 + x4 = 0 + 128 Combine like terms: 0 + 128 = 128 800i2 + -100i2x + -25i2x2 + 144x + -44x2 + x4 = 128 Add '-144x' to each side of the equation. 800i2 + -100i2x + -25i2x2 + 144x + -44x2 + -144x + x4 = 128 + -144x Reorder the terms: 800i2 + -100i2x + -25i2x2 + 144x + -144x + -44x2 + x4 = 128 + -144x Combine like terms: 144x + -144x = 0 800i2 + -100i2x + -25i2x2 + 0 + -44x2 + x4 = 128 + -144x 800i2 + -100i2x + -25i2x2 + -44x2 + x4 = 128 + -144x Add '44x2' to each side of the equation. 800i2 + -100i2x + -25i2x2 + -44x2 + 44x2 + x4 = 128 + -144x + 44x2 Combine like terms: -44x2 + 44x2 = 0 800i2 + -100i2x + -25i2x2 + 0 + x4 = 128 + -144x + 44x2 800i2 + -100i2x + -25i2x2 + x4 = 128 + -144x + 44x2 Add '-1x4' to each side of the equation. 800i2 + -100i2x + -25i2x2 + x4 + -1x4 = 128 + -144x + 44x2 + -1x4 Combine like terms: x4 + -1x4 = 0 800i2 + -100i2x + -25i2x2 + 0 = 128 + -144x + 44x2 + -1x4 800i2 + -100i2x + -25i2x2 = 128 + -144x + 44x2 + -1x4 Reorder the terms: -128 + 800i2 + -100i2x + -25i2x2 + 144x + -44x2 + x4 = 128 + -144x + 44x2 + -1x4 + -128 + 144x + -44x2 + x4 Reorder the terms: -128 + 800i2 + -100i2x + -25i2x2 + 144x + -44x2 + x4 = 128 + -128 + -144x + 144x + 44x2 + -44x2 + -1x4 + x4 Combine like terms: 128 + -128 = 0 -128 + 800i2 + -100i2x + -25i2x2 + 144x + -44x2 + x4 = 0 + -144x + 144x + 44x2 + -44x2 + -1x4 + x4 -128 + 800i2 + -100i2x + -25i2x2 + 144x + -44x2 + x4 = -144x + 144x + 44x2 + -44x2 + -1x4 + x4 Combine like terms: -144x + 144x = 0 -128 + 800i2 + -100i2x + -25i2x2 + 144x + -44x2 + x4 = 0 + 44x2 + -44x2 + -1x4 + x4 -128 + 800i2 + -100i2x + -25i2x2 + 144x + -44x2 + x4 = 44x2 + -44x2 + -1x4 + x4 Combine like terms: 44x2 + -44x2 = 0 -128 + 800i2 + -100i2x + -25i2x2 + 144x + -44x2 + x4 = 0 + -1x4 + x4 -128 + 800i2 + -100i2x + -25i2x2 + 144x + -44x2 + x4 = -1x4 + x4 Combine like terms: -1x4 + x4 = 0 -128 + 800i2 + -100i2x + -25i2x2 + 144x + -44x2 + x4 = 0 The solution to this equation could not be determined.
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