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Simplifying (x + -5)(x + 1)(x + -4 + -4i)(x + -4 + 4i) = -200 Reorder the terms: (-5 + x)(x + 1)(x + -4 + -4i)(x + -4 + 4i) = -200 Reorder the terms: (-5 + x)(1 + x)(x + -4 + -4i)(x + -4 + 4i) = -200 Reorder the terms: (-5 + x)(1 + x)(-4 + -4i + x)(x + -4 + 4i) = -200 Reorder the terms: (-5 + x)(1 + x)(-4 + -4i + x)(-4 + 4i + x) = -200 Multiply (-5 + x) * (1 + x) (-5(1 + x) + x(1 + x))(-4 + -4i + x)(-4 + 4i + x) = -200 ((1 * -5 + x * -5) + x(1 + x))(-4 + -4i + x)(-4 + 4i + x) = -200 ((-5 + -5x) + x(1 + x))(-4 + -4i + x)(-4 + 4i + x) = -200 (-5 + -5x + (1 * x + x * x))(-4 + -4i + x)(-4 + 4i + x) = -200 (-5 + -5x + (1x + x2))(-4 + -4i + x)(-4 + 4i + x) = -200 Combine like terms: -5x + 1x = -4x (-5 + -4x + x2)(-4 + -4i + x)(-4 + 4i + x) = -200 Multiply (-5 + -4x + x2) * (-4 + -4i + x) (-5(-4 + -4i + x) + -4x * (-4 + -4i + x) + x2(-4 + -4i + x))(-4 + 4i + x) = -200 ((-4 * -5 + -4i * -5 + x * -5) + -4x * (-4 + -4i + x) + x2(-4 + -4i + x))(-4 + 4i + x) = -200 ((20 + 20i + -5x) + -4x * (-4 + -4i + x) + x2(-4 + -4i + x))(-4 + 4i + x) = -200 (20 + 20i + -5x + (-4 * -4x + -4i * -4x + x * -4x) + x2(-4 + -4i + x))(-4 + 4i + x) = -200 Reorder the terms: (20 + 20i + -5x + (16ix + 16x + -4x2) + x2(-4 + -4i + x))(-4 + 4i + x) = -200 (20 + 20i + -5x + (16ix + 16x + -4x2) + x2(-4 + -4i + x))(-4 + 4i + x) = -200 (20 + 20i + -5x + 16ix + 16x + -4x2 + (-4 * x2 + -4i * x2 + x * x2))(-4 + 4i + x) = -200 Reorder the terms: (20 + 20i + -5x + 16ix + 16x + -4x2 + (-4ix2 + -4x2 + x3))(-4 + 4i + x) = -200 (20 + 20i + -5x + 16ix + 16x + -4x2 + (-4ix2 + -4x2 + x3))(-4 + 4i + x) = -200 Reorder the terms: (20 + 20i + 16ix + -4ix2 + -5x + 16x + -4x2 + -4x2 + x3)(-4 + 4i + x) = -200 Combine like terms: -5x + 16x = 11x (20 + 20i + 16ix + -4ix2 + 11x + -4x2 + -4x2 + x3)(-4 + 4i + x) = -200 Combine like terms: -4x2 + -4x2 = -8x2 (20 + 20i + 16ix + -4ix2 + 11x + -8x2 + x3)(-4 + 4i + x) = -200 Multiply (20 + 20i + 16ix + -4ix2 + 11x + -8x2 + x3) * (-4 + 4i + x) (20(-4 + 4i + x) + 20i * (-4 + 4i + x) + 16ix * (-4 + 4i + x) + -4ix2 * (-4 + 4i + x) + 11x * (-4 + 4i + x) + -8x2 * (-4 + 4i + x) + x3(-4 + 4i + x)) = -200 ((-4 * 20 + 4i * 20 + x * 20) + 20i * (-4 + 4i + x) + 16ix * (-4 + 4i + x) + -4ix2 * (-4 + 4i + x) + 11x * (-4 + 4i + x) + -8x2 * (-4 + 4i + x) + x3(-4 + 4i + x)) = -200 ((-80 + 80i + 20x) + 20i * (-4 + 4i + x) + 16ix * (-4 + 4i + x) + -4ix2 * (-4 + 4i + x) + 11x * (-4 + 4i + x) + -8x2 * (-4 + 4i + x) + x3(-4 + 4i + x)) = -200 (-80 + 80i + 20x + (-4 * 20i + 4i * 20i + x * 20i) + 16ix * (-4 + 4i + x) + -4ix2 * (-4 + 4i + x) + 11x * (-4 + 4i + x) + -8x2 * (-4 + 4i + x) + x3(-4 + 4i + x)) = -200 Reorder the terms: (-80 + 80i + 20x + (-80i + 20ix + 80i2) + 16ix * (-4 + 4i + x) + -4ix2 * (-4 + 4i + x) + 11x * (-4 + 4i + x) + -8x2 * (-4 + 4i + x) + x3(-4 + 4i + x)) = -200 (-80 + 80i + 20x + (-80i + 20ix + 80i2) + 16ix * (-4 + 4i + x) + -4ix2 * (-4 + 4i + x) + 11x * (-4 + 4i + x) + -8x2 * (-4 + 4i + x) + x3(-4 + 4i + x)) = -200 (-80 + 80i + 20x + -80i + 20ix + 80i2 + (-4 * 16ix + 4i * 16ix + x * 16ix) + -4ix2 * (-4 + 4i + x) + 11x * (-4 + 4i + x) + -8x2 * (-4 + 4i + x) + x3(-4 + 4i + x)) = -200 Reorder the terms: (-80 + 80i + 20x + -80i + 20ix + 80i2 + (-64ix + 16ix2 + 64i2x) + -4ix2 * (-4 + 4i + x) + 11x * (-4 + 4i + x) + -8x2 * (-4 + 4i + x) + x3(-4 + 4i + x)) = -200 (-80 + 80i + 20x + -80i + 20ix + 80i2 + (-64ix + 16ix2 + 64i2x) + -4ix2 * (-4 + 4i + x) + 11x * (-4 + 4i + x) + -8x2 * (-4 + 4i + x) + x3(-4 + 4i + x)) = -200 (-80 + 80i + 20x + -80i + 20ix + 80i2 + -64ix + 16ix2 + 64i2x + (-4 * -4ix2 + 4i * -4ix2 + x * -4ix2) + 11x * (-4 + 4i + x) + -8x2 * (-4 + 4i + x) + x3(-4 + 4i + x)) = -200 Reorder the terms: (-80 + 80i + 20x + -80i + 20ix + 80i2 + -64ix + 16ix2 + 64i2x + (16ix2 + -4ix3 + -16i2x2) + 11x * (-4 + 4i + x) + -8x2 * (-4 + 4i + x) + x3(-4 + 4i + x)) = -200 (-80 + 80i + 20x + -80i + 20ix + 80i2 + -64ix + 16ix2 + 64i2x + (16ix2 + -4ix3 + -16i2x2) + 11x * (-4 + 4i + x) + -8x2 * (-4 + 4i + x) + x3(-4 + 4i + x)) = -200 (-80 + 80i + 20x + -80i + 20ix + 80i2 + -64ix + 16ix2 + 64i2x + 16ix2 + -4ix3 + -16i2x2 + (-4 * 11x + 4i * 11x + x * 11x) + -8x2 * (-4 + 4i + x) + x3(-4 + 4i + x)) = -200 Reorder the terms: (-80 + 80i + 20x + -80i + 20ix + 80i2 + -64ix + 16ix2 + 64i2x + 16ix2 + -4ix3 + -16i2x2 + (44ix + -44x + 11x2) + -8x2 * (-4 + 4i + x) + x3(-4 + 4i + x)) = -200 (-80 + 80i + 20x + -80i + 20ix + 80i2 + -64ix + 16ix2 + 64i2x + 16ix2 + -4ix3 + -16i2x2 + (44ix + -44x + 11x2) + -8x2 * (-4 + 4i + x) + x3(-4 + 4i + x)) = -200 (-80 + 80i + 20x + -80i + 20ix + 80i2 + -64ix + 16ix2 + 64i2x + 16ix2 + -4ix3 + -16i2x2 + 44ix + -44x + 11x2 + (-4 * -8x2 + 4i * -8x2 + x * -8x2) + x3(-4 + 4i + x)) = -200 Reorder the terms: (-80 + 80i + 20x + -80i + 20ix + 80i2 + -64ix + 16ix2 + 64i2x + 16ix2 + -4ix3 + -16i2x2 + 44ix + -44x + 11x2 + (-32ix2 + 32x2 + -8x3) + x3(-4 + 4i + x)) = -200 (-80 + 80i + 20x + -80i + 20ix + 80i2 + -64ix + 16ix2 + 64i2x + 16ix2 + -4ix3 + -16i2x2 + 44ix + -44x + 11x2 + (-32ix2 + 32x2 + -8x3) + x3(-4 + 4i + x)) = -200 (-80 + 80i + 20x + -80i + 20ix + 80i2 + -64ix + 16ix2 + 64i2x + 16ix2 + -4ix3 + -16i2x2 + 44ix + -44x + 11x2 + -32ix2 + 32x2 + -8x3 + (-4 * x3 + 4i * x3 + x * x3)) = -200 Reorder the terms: (-80 + 80i + 20x + -80i + 20ix + 80i2 + -64ix + 16ix2 + 64i2x + 16ix2 + -4ix3 + -16i2x2 + 44ix + -44x + 11x2 + -32ix2 + 32x2 + -8x3 + (4ix3 + -4x3 + x4)) = -200 (-80 + 80i + 20x + -80i + 20ix + 80i2 + -64ix + 16ix2 + 64i2x + 16ix2 + -4ix3 + -16i2x2 + 44ix + -44x + 11x2 + -32ix2 + 32x2 + -8x3 + (4ix3 + -4x3 + x4)) = -200 Reorder the terms: (-80 + 80i + -80i + 20ix + -64ix + 44ix + 16ix2 + 16ix2 + -32ix2 + -4ix3 + 4ix3 + 80i2 + 64i2x + -16i2x2 + 20x + -44x + 11x2 + 32x2 + -8x3 + -4x3 + x4) = -200 Combine like terms: 80i + -80i = 0 (-80 + 0 + 20ix + -64ix + 44ix + 16ix2 + 16ix2 + -32ix2 + -4ix3 + 4ix3 + 80i2 + 64i2x + -16i2x2 + 20x + -44x + 11x2 + 32x2 + -8x3 + -4x3 + x4) = -200 (-80 + 20ix + -64ix + 44ix + 16ix2 + 16ix2 + -32ix2 + -4ix3 + 4ix3 + 80i2 + 64i2x + -16i2x2 + 20x + -44x + 11x2 + 32x2 + -8x3 + -4x3 + x4) = -200 Combine like terms: 20ix + -64ix = -44ix (-80 + -44ix + 44ix + 16ix2 + 16ix2 + -32ix2 + -4ix3 + 4ix3 + 80i2 + 64i2x + -16i2x2 + 20x + -44x + 11x2 + 32x2 + -8x3 + -4x3 + x4) = -200 Combine like terms: -44ix + 44ix = 0 (-80 + 0 + 16ix2 + 16ix2 + -32ix2 + -4ix3 + 4ix3 + 80i2 + 64i2x + -16i2x2 + 20x + -44x + 11x2 + 32x2 + -8x3 + -4x3 + x4) = -200 (-80 + 16ix2 + 16ix2 + -32ix2 + -4ix3 + 4ix3 + 80i2 + 64i2x + -16i2x2 + 20x + -44x + 11x2 + 32x2 + -8x3 + -4x3 + x4) = -200 Combine like terms: 16ix2 + 16ix2 = 32ix2 (-80 + 32ix2 + -32ix2 + -4ix3 + 4ix3 + 80i2 + 64i2x + -16i2x2 + 20x + -44x + 11x2 + 32x2 + -8x3 + -4x3 + x4) = -200 Combine like terms: 32ix2 + -32ix2 = 0 (-80 + 0 + -4ix3 + 4ix3 + 80i2 + 64i2x + -16i2x2 + 20x + -44x + 11x2 + 32x2 + -8x3 + -4x3 + x4) = -200 (-80 + -4ix3 + 4ix3 + 80i2 + 64i2x + -16i2x2 + 20x + -44x + 11x2 + 32x2 + -8x3 + -4x3 + x4) = -200 Combine like terms: -4ix3 + 4ix3 = 0 (-80 + 0 + 80i2 + 64i2x + -16i2x2 + 20x + -44x + 11x2 + 32x2 + -8x3 + -4x3 + x4) = -200 (-80 + 80i2 + 64i2x + -16i2x2 + 20x + -44x + 11x2 + 32x2 + -8x3 + -4x3 + x4) = -200 Combine like terms: 20x + -44x = -24x (-80 + 80i2 + 64i2x + -16i2x2 + -24x + 11x2 + 32x2 + -8x3 + -4x3 + x4) = -200 Combine like terms: 11x2 + 32x2 = 43x2 (-80 + 80i2 + 64i2x + -16i2x2 + -24x + 43x2 + -8x3 + -4x3 + x4) = -200 Combine like terms: -8x3 + -4x3 = -12x3 (-80 + 80i2 + 64i2x + -16i2x2 + -24x + 43x2 + -12x3 + x4) = -200 Solving -80 + 80i2 + 64i2x + -16i2x2 + -24x + 43x2 + -12x3 + x4 = -200 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '80' to each side of the equation. -80 + 80i2 + 64i2x + -16i2x2 + -24x + 43x2 + -12x3 + 80 + x4 = -200 + 80 Reorder the terms: -80 + 80 + 80i2 + 64i2x + -16i2x2 + -24x + 43x2 + -12x3 + x4 = -200 + 80 Combine like terms: -80 + 80 = 0 0 + 80i2 + 64i2x + -16i2x2 + -24x + 43x2 + -12x3 + x4 = -200 + 80 80i2 + 64i2x + -16i2x2 + -24x + 43x2 + -12x3 + x4 = -200 + 80 Combine like terms: -200 + 80 = -120 80i2 + 64i2x + -16i2x2 + -24x + 43x2 + -12x3 + x4 = -120 Add '24x' to each side of the equation. 80i2 + 64i2x + -16i2x2 + -24x + 43x2 + -12x3 + 24x + x4 = -120 + 24x Reorder the terms: 80i2 + 64i2x + -16i2x2 + -24x + 24x + 43x2 + -12x3 + x4 = -120 + 24x Combine like terms: -24x + 24x = 0 80i2 + 64i2x + -16i2x2 + 0 + 43x2 + -12x3 + x4 = -120 + 24x 80i2 + 64i2x + -16i2x2 + 43x2 + -12x3 + x4 = -120 + 24x Add '-43x2' to each side of the equation. 80i2 + 64i2x + -16i2x2 + 43x2 + -12x3 + -43x2 + x4 = -120 + 24x + -43x2 Reorder the terms: 80i2 + 64i2x + -16i2x2 + 43x2 + -43x2 + -12x3 + x4 = -120 + 24x + -43x2 Combine like terms: 43x2 + -43x2 = 0 80i2 + 64i2x + -16i2x2 + 0 + -12x3 + x4 = -120 + 24x + -43x2 80i2 + 64i2x + -16i2x2 + -12x3 + x4 = -120 + 24x + -43x2 Add '12x3' to each side of the equation. 80i2 + 64i2x + -16i2x2 + -12x3 + 12x3 + x4 = -120 + 24x + -43x2 + 12x3 Combine like terms: -12x3 + 12x3 = 0 80i2 + 64i2x + -16i2x2 + 0 + x4 = -120 + 24x + -43x2 + 12x3 80i2 + 64i2x + -16i2x2 + x4 = -120 + 24x + -43x2 + 12x3 Add '-1x4' to each side of the equation. 80i2 + 64i2x + -16i2x2 + x4 + -1x4 = -120 + 24x + -43x2 + 12x3 + -1x4 Combine like terms: x4 + -1x4 = 0 80i2 + 64i2x + -16i2x2 + 0 = -120 + 24x + -43x2 + 12x3 + -1x4 80i2 + 64i2x + -16i2x2 = -120 + 24x + -43x2 + 12x3 + -1x4 Reorder the terms: 120 + 80i2 + 64i2x + -16i2x2 + -24x + 43x2 + -12x3 + x4 = -120 + 24x + -43x2 + 12x3 + -1x4 + 120 + -24x + 43x2 + -12x3 + x4 Reorder the terms: 120 + 80i2 + 64i2x + -16i2x2 + -24x + 43x2 + -12x3 + x4 = -120 + 120 + 24x + -24x + -43x2 + 43x2 + 12x3 + -12x3 + -1x4 + x4 Combine like terms: -120 + 120 = 0 120 + 80i2 + 64i2x + -16i2x2 + -24x + 43x2 + -12x3 + x4 = 0 + 24x + -24x + -43x2 + 43x2 + 12x3 + -12x3 + -1x4 + x4 120 + 80i2 + 64i2x + -16i2x2 + -24x + 43x2 + -12x3 + x4 = 24x + -24x + -43x2 + 43x2 + 12x3 + -12x3 + -1x4 + x4 Combine like terms: 24x + -24x = 0 120 + 80i2 + 64i2x + -16i2x2 + -24x + 43x2 + -12x3 + x4 = 0 + -43x2 + 43x2 + 12x3 + -12x3 + -1x4 + x4 120 + 80i2 + 64i2x + -16i2x2 + -24x + 43x2 + -12x3 + x4 = -43x2 + 43x2 + 12x3 + -12x3 + -1x4 + x4 Combine like terms: -43x2 + 43x2 = 0 120 + 80i2 + 64i2x + -16i2x2 + -24x + 43x2 + -12x3 + x4 = 0 + 12x3 + -12x3 + -1x4 + x4 120 + 80i2 + 64i2x + -16i2x2 + -24x + 43x2 + -12x3 + x4 = 12x3 + -12x3 + -1x4 + x4 Combine like terms: 12x3 + -12x3 = 0 120 + 80i2 + 64i2x + -16i2x2 + -24x + 43x2 + -12x3 + x4 = 0 + -1x4 + x4 120 + 80i2 + 64i2x + -16i2x2 + -24x + 43x2 + -12x3 + x4 = -1x4 + x4 Combine like terms: -1x4 + x4 = 0 120 + 80i2 + 64i2x + -16i2x2 + -24x + 43x2 + -12x3 + x4 = 0 The solution to this equation could not be determined.
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