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Simplifying 0 = (x + 4)(x + 4 + 5i)(x + 4 + -5i) Reorder the terms: 0 = (4 + x)(x + 4 + 5i)(x + 4 + -5i) Reorder the terms: 0 = (4 + x)(4 + 5i + x)(x + 4 + -5i) Reorder the terms: 0 = (4 + x)(4 + 5i + x)(4 + -5i + x) Multiply (4 + x) * (4 + 5i + x) 0 = (4(4 + 5i + x) + x(4 + 5i + x))(4 + -5i + x) 0 = ((4 * 4 + 5i * 4 + x * 4) + x(4 + 5i + x))(4 + -5i + x) 0 = ((16 + 20i + 4x) + x(4 + 5i + x))(4 + -5i + x) 0 = (16 + 20i + 4x + (4 * x + 5i * x + x * x))(4 + -5i + x) Reorder the terms: 0 = (16 + 20i + 4x + (5ix + 4x + x2))(4 + -5i + x) 0 = (16 + 20i + 4x + (5ix + 4x + x2))(4 + -5i + x) Reorder the terms: 0 = (16 + 20i + 5ix + 4x + 4x + x2)(4 + -5i + x) Combine like terms: 4x + 4x = 8x 0 = (16 + 20i + 5ix + 8x + x2)(4 + -5i + x) Multiply (16 + 20i + 5ix + 8x + x2) * (4 + -5i + x) 0 = (16(4 + -5i + x) + 20i * (4 + -5i + x) + 5ix * (4 + -5i + x) + 8x * (4 + -5i + x) + x2(4 + -5i + x)) 0 = ((4 * 16 + -5i * 16 + x * 16) + 20i * (4 + -5i + x) + 5ix * (4 + -5i + x) + 8x * (4 + -5i + x) + x2(4 + -5i + x)) 0 = ((64 + -80i + 16x) + 20i * (4 + -5i + x) + 5ix * (4 + -5i + x) + 8x * (4 + -5i + x) + x2(4 + -5i + x)) 0 = (64 + -80i + 16x + (4 * 20i + -5i * 20i + x * 20i) + 5ix * (4 + -5i + x) + 8x * (4 + -5i + x) + x2(4 + -5i + x)) Reorder the terms: 0 = (64 + -80i + 16x + (80i + 20ix + -100i2) + 5ix * (4 + -5i + x) + 8x * (4 + -5i + x) + x2(4 + -5i + x)) 0 = (64 + -80i + 16x + (80i + 20ix + -100i2) + 5ix * (4 + -5i + x) + 8x * (4 + -5i + x) + x2(4 + -5i + x)) 0 = (64 + -80i + 16x + 80i + 20ix + -100i2 + (4 * 5ix + -5i * 5ix + x * 5ix) + 8x * (4 + -5i + x) + x2(4 + -5i + x)) Reorder the terms: 0 = (64 + -80i + 16x + 80i + 20ix + -100i2 + (20ix + 5ix2 + -25i2x) + 8x * (4 + -5i + x) + x2(4 + -5i + x)) 0 = (64 + -80i + 16x + 80i + 20ix + -100i2 + (20ix + 5ix2 + -25i2x) + 8x * (4 + -5i + x) + x2(4 + -5i + x)) 0 = (64 + -80i + 16x + 80i + 20ix + -100i2 + 20ix + 5ix2 + -25i2x + (4 * 8x + -5i * 8x + x * 8x) + x2(4 + -5i + x)) Reorder the terms: 0 = (64 + -80i + 16x + 80i + 20ix + -100i2 + 20ix + 5ix2 + -25i2x + (-40ix + 32x + 8x2) + x2(4 + -5i + x)) 0 = (64 + -80i + 16x + 80i + 20ix + -100i2 + 20ix + 5ix2 + -25i2x + (-40ix + 32x + 8x2) + x2(4 + -5i + x)) 0 = (64 + -80i + 16x + 80i + 20ix + -100i2 + 20ix + 5ix2 + -25i2x + -40ix + 32x + 8x2 + (4 * x2 + -5i * x2 + x * x2)) Reorder the terms: 0 = (64 + -80i + 16x + 80i + 20ix + -100i2 + 20ix + 5ix2 + -25i2x + -40ix + 32x + 8x2 + (-5ix2 + 4x2 + x3)) 0 = (64 + -80i + 16x + 80i + 20ix + -100i2 + 20ix + 5ix2 + -25i2x + -40ix + 32x + 8x2 + (-5ix2 + 4x2 + x3)) Reorder the terms: 0 = (64 + -80i + 80i + 20ix + 20ix + -40ix + 5ix2 + -5ix2 + -100i2 + -25i2x + 16x + 32x + 8x2 + 4x2 + x3) Combine like terms: -80i + 80i = 0 0 = (64 + 0 + 20ix + 20ix + -40ix + 5ix2 + -5ix2 + -100i2 + -25i2x + 16x + 32x + 8x2 + 4x2 + x3) 0 = (64 + 20ix + 20ix + -40ix + 5ix2 + -5ix2 + -100i2 + -25i2x + 16x + 32x + 8x2 + 4x2 + x3) Combine like terms: 20ix + 20ix = 40ix 0 = (64 + 40ix + -40ix + 5ix2 + -5ix2 + -100i2 + -25i2x + 16x + 32x + 8x2 + 4x2 + x3) Combine like terms: 40ix + -40ix = 0 0 = (64 + 0 + 5ix2 + -5ix2 + -100i2 + -25i2x + 16x + 32x + 8x2 + 4x2 + x3) 0 = (64 + 5ix2 + -5ix2 + -100i2 + -25i2x + 16x + 32x + 8x2 + 4x2 + x3) Combine like terms: 5ix2 + -5ix2 = 0 0 = (64 + 0 + -100i2 + -25i2x + 16x + 32x + 8x2 + 4x2 + x3) 0 = (64 + -100i2 + -25i2x + 16x + 32x + 8x2 + 4x2 + x3) Combine like terms: 16x + 32x = 48x 0 = (64 + -100i2 + -25i2x + 48x + 8x2 + 4x2 + x3) Combine like terms: 8x2 + 4x2 = 12x2 0 = (64 + -100i2 + -25i2x + 48x + 12x2 + x3) Solving 0 = 64 + -100i2 + -25i2x + 48x + 12x2 + x3 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '100i2' to each side of the equation. 0 + 100i2 = 64 + -100i2 + -25i2x + 48x + 12x2 + 100i2 + x3 Remove the zero: 100i2 = 64 + -100i2 + -25i2x + 48x + 12x2 + 100i2 + x3 Reorder the terms: 100i2 = 64 + -100i2 + 100i2 + -25i2x + 48x + 12x2 + x3 Combine like terms: -100i2 + 100i2 = 0 100i2 = 64 + 0 + -25i2x + 48x + 12x2 + x3 100i2 = 64 + -25i2x + 48x + 12x2 + x3 Add '25i2x' to each side of the equation. 100i2 + 25i2x = 64 + -25i2x + 48x + 12x2 + 25i2x + x3 Reorder the terms: 100i2 + 25i2x = 64 + -25i2x + 25i2x + 48x + 12x2 + x3 Combine like terms: -25i2x + 25i2x = 0 100i2 + 25i2x = 64 + 0 + 48x + 12x2 + x3 100i2 + 25i2x = 64 + 48x + 12x2 + x3 Reorder the terms: -64 + 100i2 + 25i2x + -48x + -12x2 + -1x3 = 64 + 48x + 12x2 + x3 + -64 + -48x + -12x2 + -1x3 Reorder the terms: -64 + 100i2 + 25i2x + -48x + -12x2 + -1x3 = 64 + -64 + 48x + -48x + 12x2 + -12x2 + x3 + -1x3 Combine like terms: 64 + -64 = 0 -64 + 100i2 + 25i2x + -48x + -12x2 + -1x3 = 0 + 48x + -48x + 12x2 + -12x2 + x3 + -1x3 -64 + 100i2 + 25i2x + -48x + -12x2 + -1x3 = 48x + -48x + 12x2 + -12x2 + x3 + -1x3 Combine like terms: 48x + -48x = 0 -64 + 100i2 + 25i2x + -48x + -12x2 + -1x3 = 0 + 12x2 + -12x2 + x3 + -1x3 -64 + 100i2 + 25i2x + -48x + -12x2 + -1x3 = 12x2 + -12x2 + x3 + -1x3 Combine like terms: 12x2 + -12x2 = 0 -64 + 100i2 + 25i2x + -48x + -12x2 + -1x3 = 0 + x3 + -1x3 -64 + 100i2 + 25i2x + -48x + -12x2 + -1x3 = x3 + -1x3 Combine like terms: x3 + -1x3 = 0 -64 + 100i2 + 25i2x + -48x + -12x2 + -1x3 = 0 The solution to this equation could not be determined.
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