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Simplifying 0 = (x + 4)(x + -7 + -5i)(x + -7 + 5i) Reorder the terms: 0 = (4 + x)(x + -7 + -5i)(x + -7 + 5i) Reorder the terms: 0 = (4 + x)(-7 + -5i + x)(x + -7 + 5i) Reorder the terms: 0 = (4 + x)(-7 + -5i + x)(-7 + 5i + x) Multiply (4 + x) * (-7 + -5i + x) 0 = (4(-7 + -5i + x) + x(-7 + -5i + x))(-7 + 5i + x) 0 = ((-7 * 4 + -5i * 4 + x * 4) + x(-7 + -5i + x))(-7 + 5i + x) 0 = ((-28 + -20i + 4x) + x(-7 + -5i + x))(-7 + 5i + x) 0 = (-28 + -20i + 4x + (-7 * x + -5i * x + x * x))(-7 + 5i + x) Reorder the terms: 0 = (-28 + -20i + 4x + (-5ix + -7x + x2))(-7 + 5i + x) 0 = (-28 + -20i + 4x + (-5ix + -7x + x2))(-7 + 5i + x) Reorder the terms: 0 = (-28 + -20i + -5ix + 4x + -7x + x2)(-7 + 5i + x) Combine like terms: 4x + -7x = -3x 0 = (-28 + -20i + -5ix + -3x + x2)(-7 + 5i + x) Multiply (-28 + -20i + -5ix + -3x + x2) * (-7 + 5i + x) 0 = (-28(-7 + 5i + x) + -20i * (-7 + 5i + x) + -5ix * (-7 + 5i + x) + -3x * (-7 + 5i + x) + x2(-7 + 5i + x)) 0 = ((-7 * -28 + 5i * -28 + x * -28) + -20i * (-7 + 5i + x) + -5ix * (-7 + 5i + x) + -3x * (-7 + 5i + x) + x2(-7 + 5i + x)) 0 = ((196 + -140i + -28x) + -20i * (-7 + 5i + x) + -5ix * (-7 + 5i + x) + -3x * (-7 + 5i + x) + x2(-7 + 5i + x)) 0 = (196 + -140i + -28x + (-7 * -20i + 5i * -20i + x * -20i) + -5ix * (-7 + 5i + x) + -3x * (-7 + 5i + x) + x2(-7 + 5i + x)) Reorder the terms: 0 = (196 + -140i + -28x + (140i + -20ix + -100i2) + -5ix * (-7 + 5i + x) + -3x * (-7 + 5i + x) + x2(-7 + 5i + x)) 0 = (196 + -140i + -28x + (140i + -20ix + -100i2) + -5ix * (-7 + 5i + x) + -3x * (-7 + 5i + x) + x2(-7 + 5i + x)) 0 = (196 + -140i + -28x + 140i + -20ix + -100i2 + (-7 * -5ix + 5i * -5ix + x * -5ix) + -3x * (-7 + 5i + x) + x2(-7 + 5i + x)) Reorder the terms: 0 = (196 + -140i + -28x + 140i + -20ix + -100i2 + (35ix + -5ix2 + -25i2x) + -3x * (-7 + 5i + x) + x2(-7 + 5i + x)) 0 = (196 + -140i + -28x + 140i + -20ix + -100i2 + (35ix + -5ix2 + -25i2x) + -3x * (-7 + 5i + x) + x2(-7 + 5i + x)) 0 = (196 + -140i + -28x + 140i + -20ix + -100i2 + 35ix + -5ix2 + -25i2x + (-7 * -3x + 5i * -3x + x * -3x) + x2(-7 + 5i + x)) Reorder the terms: 0 = (196 + -140i + -28x + 140i + -20ix + -100i2 + 35ix + -5ix2 + -25i2x + (-15ix + 21x + -3x2) + x2(-7 + 5i + x)) 0 = (196 + -140i + -28x + 140i + -20ix + -100i2 + 35ix + -5ix2 + -25i2x + (-15ix + 21x + -3x2) + x2(-7 + 5i + x)) 0 = (196 + -140i + -28x + 140i + -20ix + -100i2 + 35ix + -5ix2 + -25i2x + -15ix + 21x + -3x2 + (-7 * x2 + 5i * x2 + x * x2)) Reorder the terms: 0 = (196 + -140i + -28x + 140i + -20ix + -100i2 + 35ix + -5ix2 + -25i2x + -15ix + 21x + -3x2 + (5ix2 + -7x2 + x3)) 0 = (196 + -140i + -28x + 140i + -20ix + -100i2 + 35ix + -5ix2 + -25i2x + -15ix + 21x + -3x2 + (5ix2 + -7x2 + x3)) Reorder the terms: 0 = (196 + -140i + 140i + -20ix + 35ix + -15ix + -5ix2 + 5ix2 + -100i2 + -25i2x + -28x + 21x + -3x2 + -7x2 + x3) Combine like terms: -140i + 140i = 0 0 = (196 + 0 + -20ix + 35ix + -15ix + -5ix2 + 5ix2 + -100i2 + -25i2x + -28x + 21x + -3x2 + -7x2 + x3) 0 = (196 + -20ix + 35ix + -15ix + -5ix2 + 5ix2 + -100i2 + -25i2x + -28x + 21x + -3x2 + -7x2 + x3) Combine like terms: -20ix + 35ix = 15ix 0 = (196 + 15ix + -15ix + -5ix2 + 5ix2 + -100i2 + -25i2x + -28x + 21x + -3x2 + -7x2 + x3) Combine like terms: 15ix + -15ix = 0 0 = (196 + 0 + -5ix2 + 5ix2 + -100i2 + -25i2x + -28x + 21x + -3x2 + -7x2 + x3) 0 = (196 + -5ix2 + 5ix2 + -100i2 + -25i2x + -28x + 21x + -3x2 + -7x2 + x3) Combine like terms: -5ix2 + 5ix2 = 0 0 = (196 + 0 + -100i2 + -25i2x + -28x + 21x + -3x2 + -7x2 + x3) 0 = (196 + -100i2 + -25i2x + -28x + 21x + -3x2 + -7x2 + x3) Combine like terms: -28x + 21x = -7x 0 = (196 + -100i2 + -25i2x + -7x + -3x2 + -7x2 + x3) Combine like terms: -3x2 + -7x2 = -10x2 0 = (196 + -100i2 + -25i2x + -7x + -10x2 + x3) Solving 0 = 196 + -100i2 + -25i2x + -7x + -10x2 + 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 = 196 + -100i2 + -25i2x + -7x + -10x2 + 100i2 + x3 Remove the zero: 100i2 = 196 + -100i2 + -25i2x + -7x + -10x2 + 100i2 + x3 Reorder the terms: 100i2 = 196 + -100i2 + 100i2 + -25i2x + -7x + -10x2 + x3 Combine like terms: -100i2 + 100i2 = 0 100i2 = 196 + 0 + -25i2x + -7x + -10x2 + x3 100i2 = 196 + -25i2x + -7x + -10x2 + x3 Add '25i2x' to each side of the equation. 100i2 + 25i2x = 196 + -25i2x + -7x + -10x2 + 25i2x + x3 Reorder the terms: 100i2 + 25i2x = 196 + -25i2x + 25i2x + -7x + -10x2 + x3 Combine like terms: -25i2x + 25i2x = 0 100i2 + 25i2x = 196 + 0 + -7x + -10x2 + x3 100i2 + 25i2x = 196 + -7x + -10x2 + x3 Reorder the terms: -196 + 100i2 + 25i2x + 7x + 10x2 + -1x3 = 196 + -7x + -10x2 + x3 + -196 + 7x + 10x2 + -1x3 Reorder the terms: -196 + 100i2 + 25i2x + 7x + 10x2 + -1x3 = 196 + -196 + -7x + 7x + -10x2 + 10x2 + x3 + -1x3 Combine like terms: 196 + -196 = 0 -196 + 100i2 + 25i2x + 7x + 10x2 + -1x3 = 0 + -7x + 7x + -10x2 + 10x2 + x3 + -1x3 -196 + 100i2 + 25i2x + 7x + 10x2 + -1x3 = -7x + 7x + -10x2 + 10x2 + x3 + -1x3 Combine like terms: -7x + 7x = 0 -196 + 100i2 + 25i2x + 7x + 10x2 + -1x3 = 0 + -10x2 + 10x2 + x3 + -1x3 -196 + 100i2 + 25i2x + 7x + 10x2 + -1x3 = -10x2 + 10x2 + x3 + -1x3 Combine like terms: -10x2 + 10x2 = 0 -196 + 100i2 + 25i2x + 7x + 10x2 + -1x3 = 0 + x3 + -1x3 -196 + 100i2 + 25i2x + 7x + 10x2 + -1x3 = x3 + -1x3 Combine like terms: x3 + -1x3 = 0 -196 + 100i2 + 25i2x + 7x + 10x2 + -1x3 = 0 The solution to this equation could not be determined.
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