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Simplifying (x + 1)(x + -1(4 + -5i))(x + -1(4 + 5i)) = 0 Reorder the terms: (1 + x)(x + -1(4 + -5i))(x + -1(4 + 5i)) = 0 (1 + x)(x + (4 * -1 + -5i * -1))(x + -1(4 + 5i)) = 0 (1 + x)(x + (-4 + 5i))(x + -1(4 + 5i)) = 0 Reorder the terms: (1 + x)(-4 + 5i + x)(x + -1(4 + 5i)) = 0 (1 + x)(-4 + 5i + x)(x + (4 * -1 + 5i * -1)) = 0 (1 + x)(-4 + 5i + x)(x + (-4 + -5i)) = 0 Reorder the terms: (1 + x)(-4 + 5i + x)(-4 + -5i + x) = 0 Multiply (1 + x) * (-4 + 5i + x) (1(-4 + 5i + x) + x(-4 + 5i + x))(-4 + -5i + x) = 0 ((-4 * 1 + 5i * 1 + x * 1) + x(-4 + 5i + x))(-4 + -5i + x) = 0 ((-4 + 5i + 1x) + x(-4 + 5i + x))(-4 + -5i + x) = 0 (-4 + 5i + 1x + (-4 * x + 5i * x + x * x))(-4 + -5i + x) = 0 Reorder the terms: (-4 + 5i + 1x + (5ix + -4x + x2))(-4 + -5i + x) = 0 (-4 + 5i + 1x + (5ix + -4x + x2))(-4 + -5i + x) = 0 Reorder the terms: (-4 + 5i + 5ix + 1x + -4x + x2)(-4 + -5i + x) = 0 Combine like terms: 1x + -4x = -3x (-4 + 5i + 5ix + -3x + x2)(-4 + -5i + x) = 0 Multiply (-4 + 5i + 5ix + -3x + x2) * (-4 + -5i + x) (-4(-4 + -5i + x) + 5i * (-4 + -5i + x) + 5ix * (-4 + -5i + x) + -3x * (-4 + -5i + x) + x2(-4 + -5i + x)) = 0 ((-4 * -4 + -5i * -4 + x * -4) + 5i * (-4 + -5i + x) + 5ix * (-4 + -5i + x) + -3x * (-4 + -5i + x) + x2(-4 + -5i + x)) = 0 ((16 + 20i + -4x) + 5i * (-4 + -5i + x) + 5ix * (-4 + -5i + x) + -3x * (-4 + -5i + x) + x2(-4 + -5i + x)) = 0 (16 + 20i + -4x + (-4 * 5i + -5i * 5i + x * 5i) + 5ix * (-4 + -5i + x) + -3x * (-4 + -5i + x) + x2(-4 + -5i + x)) = 0 Reorder the terms: (16 + 20i + -4x + (-20i + 5ix + -25i2) + 5ix * (-4 + -5i + x) + -3x * (-4 + -5i + x) + x2(-4 + -5i + x)) = 0 (16 + 20i + -4x + (-20i + 5ix + -25i2) + 5ix * (-4 + -5i + x) + -3x * (-4 + -5i + x) + x2(-4 + -5i + x)) = 0 (16 + 20i + -4x + -20i + 5ix + -25i2 + (-4 * 5ix + -5i * 5ix + x * 5ix) + -3x * (-4 + -5i + x) + x2(-4 + -5i + x)) = 0 Reorder the terms: (16 + 20i + -4x + -20i + 5ix + -25i2 + (-20ix + 5ix2 + -25i2x) + -3x * (-4 + -5i + x) + x2(-4 + -5i + x)) = 0 (16 + 20i + -4x + -20i + 5ix + -25i2 + (-20ix + 5ix2 + -25i2x) + -3x * (-4 + -5i + x) + x2(-4 + -5i + x)) = 0 (16 + 20i + -4x + -20i + 5ix + -25i2 + -20ix + 5ix2 + -25i2x + (-4 * -3x + -5i * -3x + x * -3x) + x2(-4 + -5i + x)) = 0 Reorder the terms: (16 + 20i + -4x + -20i + 5ix + -25i2 + -20ix + 5ix2 + -25i2x + (15ix + 12x + -3x2) + x2(-4 + -5i + x)) = 0 (16 + 20i + -4x + -20i + 5ix + -25i2 + -20ix + 5ix2 + -25i2x + (15ix + 12x + -3x2) + x2(-4 + -5i + x)) = 0 (16 + 20i + -4x + -20i + 5ix + -25i2 + -20ix + 5ix2 + -25i2x + 15ix + 12x + -3x2 + (-4 * x2 + -5i * x2 + x * x2)) = 0 Reorder the terms: (16 + 20i + -4x + -20i + 5ix + -25i2 + -20ix + 5ix2 + -25i2x + 15ix + 12x + -3x2 + (-5ix2 + -4x2 + x3)) = 0 (16 + 20i + -4x + -20i + 5ix + -25i2 + -20ix + 5ix2 + -25i2x + 15ix + 12x + -3x2 + (-5ix2 + -4x2 + x3)) = 0 Reorder the terms: (16 + 20i + -20i + 5ix + -20ix + 15ix + 5ix2 + -5ix2 + -25i2 + -25i2x + -4x + 12x + -3x2 + -4x2 + x3) = 0 Combine like terms: 20i + -20i = 0 (16 + 0 + 5ix + -20ix + 15ix + 5ix2 + -5ix2 + -25i2 + -25i2x + -4x + 12x + -3x2 + -4x2 + x3) = 0 (16 + 5ix + -20ix + 15ix + 5ix2 + -5ix2 + -25i2 + -25i2x + -4x + 12x + -3x2 + -4x2 + x3) = 0 Combine like terms: 5ix + -20ix = -15ix (16 + -15ix + 15ix + 5ix2 + -5ix2 + -25i2 + -25i2x + -4x + 12x + -3x2 + -4x2 + x3) = 0 Combine like terms: -15ix + 15ix = 0 (16 + 0 + 5ix2 + -5ix2 + -25i2 + -25i2x + -4x + 12x + -3x2 + -4x2 + x3) = 0 (16 + 5ix2 + -5ix2 + -25i2 + -25i2x + -4x + 12x + -3x2 + -4x2 + x3) = 0 Combine like terms: 5ix2 + -5ix2 = 0 (16 + 0 + -25i2 + -25i2x + -4x + 12x + -3x2 + -4x2 + x3) = 0 (16 + -25i2 + -25i2x + -4x + 12x + -3x2 + -4x2 + x3) = 0 Combine like terms: -4x + 12x = 8x (16 + -25i2 + -25i2x + 8x + -3x2 + -4x2 + x3) = 0 Combine like terms: -3x2 + -4x2 = -7x2 (16 + -25i2 + -25i2x + 8x + -7x2 + x3) = 0 Solving 16 + -25i2 + -25i2x + 8x + -7x2 + x3 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -25i2 + -25i2x + 8x + -7x2 + -16 + x3 = 0 + -16 Reorder the terms: 16 + -16 + -25i2 + -25i2x + 8x + -7x2 + x3 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -25i2 + -25i2x + 8x + -7x2 + x3 = 0 + -16 -25i2 + -25i2x + 8x + -7x2 + x3 = 0 + -16 Combine like terms: 0 + -16 = -16 -25i2 + -25i2x + 8x + -7x2 + x3 = -16 Add '-8x' to each side of the equation. -25i2 + -25i2x + 8x + -7x2 + -8x + x3 = -16 + -8x Reorder the terms: -25i2 + -25i2x + 8x + -8x + -7x2 + x3 = -16 + -8x Combine like terms: 8x + -8x = 0 -25i2 + -25i2x + 0 + -7x2 + x3 = -16 + -8x -25i2 + -25i2x + -7x2 + x3 = -16 + -8x Add '7x2' to each side of the equation. -25i2 + -25i2x + -7x2 + 7x2 + x3 = -16 + -8x + 7x2 Combine like terms: -7x2 + 7x2 = 0 -25i2 + -25i2x + 0 + x3 = -16 + -8x + 7x2 -25i2 + -25i2x + x3 = -16 + -8x + 7x2 Add '-1x3' to each side of the equation. -25i2 + -25i2x + x3 + -1x3 = -16 + -8x + 7x2 + -1x3 Combine like terms: x3 + -1x3 = 0 -25i2 + -25i2x + 0 = -16 + -8x + 7x2 + -1x3 -25i2 + -25i2x = -16 + -8x + 7x2 + -1x3 Reorder the terms: 16 + -25i2 + -25i2x + 8x + -7x2 + x3 = -16 + -8x + 7x2 + -1x3 + 16 + 8x + -7x2 + x3 Reorder the terms: 16 + -25i2 + -25i2x + 8x + -7x2 + x3 = -16 + 16 + -8x + 8x + 7x2 + -7x2 + -1x3 + x3 Combine like terms: -16 + 16 = 0 16 + -25i2 + -25i2x + 8x + -7x2 + x3 = 0 + -8x + 8x + 7x2 + -7x2 + -1x3 + x3 16 + -25i2 + -25i2x + 8x + -7x2 + x3 = -8x + 8x + 7x2 + -7x2 + -1x3 + x3 Combine like terms: -8x + 8x = 0 16 + -25i2 + -25i2x + 8x + -7x2 + x3 = 0 + 7x2 + -7x2 + -1x3 + x3 16 + -25i2 + -25i2x + 8x + -7x2 + x3 = 7x2 + -7x2 + -1x3 + x3 Combine like terms: 7x2 + -7x2 = 0 16 + -25i2 + -25i2x + 8x + -7x2 + x3 = 0 + -1x3 + x3 16 + -25i2 + -25i2x + 8x + -7x2 + x3 = -1x3 + x3 Combine like terms: -1x3 + x3 = 0 16 + -25i2 + -25i2x + 8x + -7x2 + x3 = 0 The solution to this equation could not be determined.
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