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Simplifying (x + 1)(x + 1)(x + -3 + 5i)(x + -3 + -5i) = 0 Reorder the terms: (1 + x)(x + 1)(x + -3 + 5i)(x + -3 + -5i) = 0 Reorder the terms: (1 + x)(1 + x)(x + -3 + 5i)(x + -3 + -5i) = 0 Reorder the terms: (1 + x)(1 + x)(-3 + 5i + x)(x + -3 + -5i) = 0 Reorder the terms: (1 + x)(1 + x)(-3 + 5i + x)(-3 + -5i + x) = 0 Multiply (1 + x) * (1 + x) (1(1 + x) + x(1 + x))(-3 + 5i + x)(-3 + -5i + x) = 0 ((1 * 1 + x * 1) + x(1 + x))(-3 + 5i + x)(-3 + -5i + x) = 0 ((1 + 1x) + x(1 + x))(-3 + 5i + x)(-3 + -5i + x) = 0 (1 + 1x + (1 * x + x * x))(-3 + 5i + x)(-3 + -5i + x) = 0 (1 + 1x + (1x + x2))(-3 + 5i + x)(-3 + -5i + x) = 0 Combine like terms: 1x + 1x = 2x (1 + 2x + x2)(-3 + 5i + x)(-3 + -5i + x) = 0 Multiply (1 + 2x + x2) * (-3 + 5i + x) (1(-3 + 5i + x) + 2x * (-3 + 5i + x) + x2(-3 + 5i + x))(-3 + -5i + x) = 0 ((-3 * 1 + 5i * 1 + x * 1) + 2x * (-3 + 5i + x) + x2(-3 + 5i + x))(-3 + -5i + x) = 0 ((-3 + 5i + 1x) + 2x * (-3 + 5i + x) + x2(-3 + 5i + x))(-3 + -5i + x) = 0 (-3 + 5i + 1x + (-3 * 2x + 5i * 2x + x * 2x) + x2(-3 + 5i + x))(-3 + -5i + x) = 0 Reorder the terms: (-3 + 5i + 1x + (10ix + -6x + 2x2) + x2(-3 + 5i + x))(-3 + -5i + x) = 0 (-3 + 5i + 1x + (10ix + -6x + 2x2) + x2(-3 + 5i + x))(-3 + -5i + x) = 0 (-3 + 5i + 1x + 10ix + -6x + 2x2 + (-3 * x2 + 5i * x2 + x * x2))(-3 + -5i + x) = 0 Reorder the terms: (-3 + 5i + 1x + 10ix + -6x + 2x2 + (5ix2 + -3x2 + x3))(-3 + -5i + x) = 0 (-3 + 5i + 1x + 10ix + -6x + 2x2 + (5ix2 + -3x2 + x3))(-3 + -5i + x) = 0 Reorder the terms: (-3 + 5i + 10ix + 5ix2 + 1x + -6x + 2x2 + -3x2 + x3)(-3 + -5i + x) = 0 Combine like terms: 1x + -6x = -5x (-3 + 5i + 10ix + 5ix2 + -5x + 2x2 + -3x2 + x3)(-3 + -5i + x) = 0 Combine like terms: 2x2 + -3x2 = -1x2 (-3 + 5i + 10ix + 5ix2 + -5x + -1x2 + x3)(-3 + -5i + x) = 0 Multiply (-3 + 5i + 10ix + 5ix2 + -5x + -1x2 + x3) * (-3 + -5i + x) (-3(-3 + -5i + x) + 5i * (-3 + -5i + x) + 10ix * (-3 + -5i + x) + 5ix2 * (-3 + -5i + x) + -5x * (-3 + -5i + x) + -1x2 * (-3 + -5i + x) + x3(-3 + -5i + x)) = 0 ((-3 * -3 + -5i * -3 + x * -3) + 5i * (-3 + -5i + x) + 10ix * (-3 + -5i + x) + 5ix2 * (-3 + -5i + x) + -5x * (-3 + -5i + x) + -1x2 * (-3 + -5i + x) + x3(-3 + -5i + x)) = 0 ((9 + 15i + -3x) + 5i * (-3 + -5i + x) + 10ix * (-3 + -5i + x) + 5ix2 * (-3 + -5i + x) + -5x * (-3 + -5i + x) + -1x2 * (-3 + -5i + x) + x3(-3 + -5i + x)) = 0 (9 + 15i + -3x + (-3 * 5i + -5i * 5i + x * 5i) + 10ix * (-3 + -5i + x) + 5ix2 * (-3 + -5i + x) + -5x * (-3 + -5i + x) + -1x2 * (-3 + -5i + x) + x3(-3 + -5i + x)) = 0 Reorder the terms: (9 + 15i + -3x + (-15i + 5ix + -25i2) + 10ix * (-3 + -5i + x) + 5ix2 * (-3 + -5i + x) + -5x * (-3 + -5i + x) + -1x2 * (-3 + -5i + x) + x3(-3 + -5i + x)) = 0 (9 + 15i + -3x + (-15i + 5ix + -25i2) + 10ix * (-3 + -5i + x) + 5ix2 * (-3 + -5i + x) + -5x * (-3 + -5i + x) + -1x2 * (-3 + -5i + x) + x3(-3 + -5i + x)) = 0 (9 + 15i + -3x + -15i + 5ix + -25i2 + (-3 * 10ix + -5i * 10ix + x * 10ix) + 5ix2 * (-3 + -5i + x) + -5x * (-3 + -5i + x) + -1x2 * (-3 + -5i + x) + x3(-3 + -5i + x)) = 0 Reorder the terms: (9 + 15i + -3x + -15i + 5ix + -25i2 + (-30ix + 10ix2 + -50i2x) + 5ix2 * (-3 + -5i + x) + -5x * (-3 + -5i + x) + -1x2 * (-3 + -5i + x) + x3(-3 + -5i + x)) = 0 (9 + 15i + -3x + -15i + 5ix + -25i2 + (-30ix + 10ix2 + -50i2x) + 5ix2 * (-3 + -5i + x) + -5x * (-3 + -5i + x) + -1x2 * (-3 + -5i + x) + x3(-3 + -5i + x)) = 0 (9 + 15i + -3x + -15i + 5ix + -25i2 + -30ix + 10ix2 + -50i2x + (-3 * 5ix2 + -5i * 5ix2 + x * 5ix2) + -5x * (-3 + -5i + x) + -1x2 * (-3 + -5i + x) + x3(-3 + -5i + x)) = 0 Reorder the terms: (9 + 15i + -3x + -15i + 5ix + -25i2 + -30ix + 10ix2 + -50i2x + (-15ix2 + 5ix3 + -25i2x2) + -5x * (-3 + -5i + x) + -1x2 * (-3 + -5i + x) + x3(-3 + -5i + x)) = 0 (9 + 15i + -3x + -15i + 5ix + -25i2 + -30ix + 10ix2 + -50i2x + (-15ix2 + 5ix3 + -25i2x2) + -5x * (-3 + -5i + x) + -1x2 * (-3 + -5i + x) + x3(-3 + -5i + x)) = 0 (9 + 15i + -3x + -15i + 5ix + -25i2 + -30ix + 10ix2 + -50i2x + -15ix2 + 5ix3 + -25i2x2 + (-3 * -5x + -5i * -5x + x * -5x) + -1x2 * (-3 + -5i + x) + x3(-3 + -5i + x)) = 0 Reorder the terms: (9 + 15i + -3x + -15i + 5ix + -25i2 + -30ix + 10ix2 + -50i2x + -15ix2 + 5ix3 + -25i2x2 + (25ix + 15x + -5x2) + -1x2 * (-3 + -5i + x) + x3(-3 + -5i + x)) = 0 (9 + 15i + -3x + -15i + 5ix + -25i2 + -30ix + 10ix2 + -50i2x + -15ix2 + 5ix3 + -25i2x2 + (25ix + 15x + -5x2) + -1x2 * (-3 + -5i + x) + x3(-3 + -5i + x)) = 0 (9 + 15i + -3x + -15i + 5ix + -25i2 + -30ix + 10ix2 + -50i2x + -15ix2 + 5ix3 + -25i2x2 + 25ix + 15x + -5x2 + (-3 * -1x2 + -5i * -1x2 + x * -1x2) + x3(-3 + -5i + x)) = 0 Reorder the terms: (9 + 15i + -3x + -15i + 5ix + -25i2 + -30ix + 10ix2 + -50i2x + -15ix2 + 5ix3 + -25i2x2 + 25ix + 15x + -5x2 + (5ix2 + 3x2 + -1x3) + x3(-3 + -5i + x)) = 0 (9 + 15i + -3x + -15i + 5ix + -25i2 + -30ix + 10ix2 + -50i2x + -15ix2 + 5ix3 + -25i2x2 + 25ix + 15x + -5x2 + (5ix2 + 3x2 + -1x3) + x3(-3 + -5i + x)) = 0 (9 + 15i + -3x + -15i + 5ix + -25i2 + -30ix + 10ix2 + -50i2x + -15ix2 + 5ix3 + -25i2x2 + 25ix + 15x + -5x2 + 5ix2 + 3x2 + -1x3 + (-3 * x3 + -5i * x3 + x * x3)) = 0 Reorder the terms: (9 + 15i + -3x + -15i + 5ix + -25i2 + -30ix + 10ix2 + -50i2x + -15ix2 + 5ix3 + -25i2x2 + 25ix + 15x + -5x2 + 5ix2 + 3x2 + -1x3 + (-5ix3 + -3x3 + x4)) = 0 (9 + 15i + -3x + -15i + 5ix + -25i2 + -30ix + 10ix2 + -50i2x + -15ix2 + 5ix3 + -25i2x2 + 25ix + 15x + -5x2 + 5ix2 + 3x2 + -1x3 + (-5ix3 + -3x3 + x4)) = 0 Reorder the terms: (9 + 15i + -15i + 5ix + -30ix + 25ix + 10ix2 + -15ix2 + 5ix2 + 5ix3 + -5ix3 + -25i2 + -50i2x + -25i2x2 + -3x + 15x + -5x2 + 3x2 + -1x3 + -3x3 + x4) = 0 Combine like terms: 15i + -15i = 0 (9 + 0 + 5ix + -30ix + 25ix + 10ix2 + -15ix2 + 5ix2 + 5ix3 + -5ix3 + -25i2 + -50i2x + -25i2x2 + -3x + 15x + -5x2 + 3x2 + -1x3 + -3x3 + x4) = 0 (9 + 5ix + -30ix + 25ix + 10ix2 + -15ix2 + 5ix2 + 5ix3 + -5ix3 + -25i2 + -50i2x + -25i2x2 + -3x + 15x + -5x2 + 3x2 + -1x3 + -3x3 + x4) = 0 Combine like terms: 5ix + -30ix = -25ix (9 + -25ix + 25ix + 10ix2 + -15ix2 + 5ix2 + 5ix3 + -5ix3 + -25i2 + -50i2x + -25i2x2 + -3x + 15x + -5x2 + 3x2 + -1x3 + -3x3 + x4) = 0 Combine like terms: -25ix + 25ix = 0 (9 + 0 + 10ix2 + -15ix2 + 5ix2 + 5ix3 + -5ix3 + -25i2 + -50i2x + -25i2x2 + -3x + 15x + -5x2 + 3x2 + -1x3 + -3x3 + x4) = 0 (9 + 10ix2 + -15ix2 + 5ix2 + 5ix3 + -5ix3 + -25i2 + -50i2x + -25i2x2 + -3x + 15x + -5x2 + 3x2 + -1x3 + -3x3 + x4) = 0 Combine like terms: 10ix2 + -15ix2 = -5ix2 (9 + -5ix2 + 5ix2 + 5ix3 + -5ix3 + -25i2 + -50i2x + -25i2x2 + -3x + 15x + -5x2 + 3x2 + -1x3 + -3x3 + x4) = 0 Combine like terms: -5ix2 + 5ix2 = 0 (9 + 0 + 5ix3 + -5ix3 + -25i2 + -50i2x + -25i2x2 + -3x + 15x + -5x2 + 3x2 + -1x3 + -3x3 + x4) = 0 (9 + 5ix3 + -5ix3 + -25i2 + -50i2x + -25i2x2 + -3x + 15x + -5x2 + 3x2 + -1x3 + -3x3 + x4) = 0 Combine like terms: 5ix3 + -5ix3 = 0 (9 + 0 + -25i2 + -50i2x + -25i2x2 + -3x + 15x + -5x2 + 3x2 + -1x3 + -3x3 + x4) = 0 (9 + -25i2 + -50i2x + -25i2x2 + -3x + 15x + -5x2 + 3x2 + -1x3 + -3x3 + x4) = 0 Combine like terms: -3x + 15x = 12x (9 + -25i2 + -50i2x + -25i2x2 + 12x + -5x2 + 3x2 + -1x3 + -3x3 + x4) = 0 Combine like terms: -5x2 + 3x2 = -2x2 (9 + -25i2 + -50i2x + -25i2x2 + 12x + -2x2 + -1x3 + -3x3 + x4) = 0 Combine like terms: -1x3 + -3x3 = -4x3 (9 + -25i2 + -50i2x + -25i2x2 + 12x + -2x2 + -4x3 + x4) = 0 Solving 9 + -25i2 + -50i2x + -25i2x2 + 12x + -2x2 + -4x3 + x4 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -25i2 + -50i2x + -25i2x2 + 12x + -2x2 + -4x3 + -9 + x4 = 0 + -9 Reorder the terms: 9 + -9 + -25i2 + -50i2x + -25i2x2 + 12x + -2x2 + -4x3 + x4 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -25i2 + -50i2x + -25i2x2 + 12x + -2x2 + -4x3 + x4 = 0 + -9 -25i2 + -50i2x + -25i2x2 + 12x + -2x2 + -4x3 + x4 = 0 + -9 Combine like terms: 0 + -9 = -9 -25i2 + -50i2x + -25i2x2 + 12x + -2x2 + -4x3 + x4 = -9 Add '-12x' to each side of the equation. -25i2 + -50i2x + -25i2x2 + 12x + -2x2 + -4x3 + -12x + x4 = -9 + -12x Reorder the terms: -25i2 + -50i2x + -25i2x2 + 12x + -12x + -2x2 + -4x3 + x4 = -9 + -12x Combine like terms: 12x + -12x = 0 -25i2 + -50i2x + -25i2x2 + 0 + -2x2 + -4x3 + x4 = -9 + -12x -25i2 + -50i2x + -25i2x2 + -2x2 + -4x3 + x4 = -9 + -12x Add '2x2' to each side of the equation. -25i2 + -50i2x + -25i2x2 + -2x2 + -4x3 + 2x2 + x4 = -9 + -12x + 2x2 Reorder the terms: -25i2 + -50i2x + -25i2x2 + -2x2 + 2x2 + -4x3 + x4 = -9 + -12x + 2x2 Combine like terms: -2x2 + 2x2 = 0 -25i2 + -50i2x + -25i2x2 + 0 + -4x3 + x4 = -9 + -12x + 2x2 -25i2 + -50i2x + -25i2x2 + -4x3 + x4 = -9 + -12x + 2x2 Add '4x3' to each side of the equation. -25i2 + -50i2x + -25i2x2 + -4x3 + 4x3 + x4 = -9 + -12x + 2x2 + 4x3 Combine like terms: -4x3 + 4x3 = 0 -25i2 + -50i2x + -25i2x2 + 0 + x4 = -9 + -12x + 2x2 + 4x3 -25i2 + -50i2x + -25i2x2 + x4 = -9 + -12x + 2x2 + 4x3 Add '-1x4' to each side of the equation. -25i2 + -50i2x + -25i2x2 + x4 + -1x4 = -9 + -12x + 2x2 + 4x3 + -1x4 Combine like terms: x4 + -1x4 = 0 -25i2 + -50i2x + -25i2x2 + 0 = -9 + -12x + 2x2 + 4x3 + -1x4 -25i2 + -50i2x + -25i2x2 = -9 + -12x + 2x2 + 4x3 + -1x4 Reorder the terms: 9 + -25i2 + -50i2x + -25i2x2 + 12x + -2x2 + -4x3 + x4 = -9 + -12x + 2x2 + 4x3 + -1x4 + 9 + 12x + -2x2 + -4x3 + x4 Reorder the terms: 9 + -25i2 + -50i2x + -25i2x2 + 12x + -2x2 + -4x3 + x4 = -9 + 9 + -12x + 12x + 2x2 + -2x2 + 4x3 + -4x3 + -1x4 + x4 Combine like terms: -9 + 9 = 0 9 + -25i2 + -50i2x + -25i2x2 + 12x + -2x2 + -4x3 + x4 = 0 + -12x + 12x + 2x2 + -2x2 + 4x3 + -4x3 + -1x4 + x4 9 + -25i2 + -50i2x + -25i2x2 + 12x + -2x2 + -4x3 + x4 = -12x + 12x + 2x2 + -2x2 + 4x3 + -4x3 + -1x4 + x4 Combine like terms: -12x + 12x = 0 9 + -25i2 + -50i2x + -25i2x2 + 12x + -2x2 + -4x3 + x4 = 0 + 2x2 + -2x2 + 4x3 + -4x3 + -1x4 + x4 9 + -25i2 + -50i2x + -25i2x2 + 12x + -2x2 + -4x3 + x4 = 2x2 + -2x2 + 4x3 + -4x3 + -1x4 + x4 Combine like terms: 2x2 + -2x2 = 0 9 + -25i2 + -50i2x + -25i2x2 + 12x + -2x2 + -4x3 + x4 = 0 + 4x3 + -4x3 + -1x4 + x4 9 + -25i2 + -50i2x + -25i2x2 + 12x + -2x2 + -4x3 + x4 = 4x3 + -4x3 + -1x4 + x4 Combine like terms: 4x3 + -4x3 = 0 9 + -25i2 + -50i2x + -25i2x2 + 12x + -2x2 + -4x3 + x4 = 0 + -1x4 + x4 9 + -25i2 + -50i2x + -25i2x2 + 12x + -2x2 + -4x3 + x4 = -1x4 + x4 Combine like terms: -1x4 + x4 = 0 9 + -25i2 + -50i2x + -25i2x2 + 12x + -2x2 + -4x3 + x4 = 0 The solution to this equation could not be determined.
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