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Simplifying (x + -5 + -7i)(x + -5 + 7i) = 0 Reorder the terms: (-5 + -7i + x)(x + -5 + 7i) = 0 Reorder the terms: (-5 + -7i + x)(-5 + 7i + x) = 0 Multiply (-5 + -7i + x) * (-5 + 7i + x) (-5(-5 + 7i + x) + -7i * (-5 + 7i + x) + x(-5 + 7i + x)) = 0 ((-5 * -5 + 7i * -5 + x * -5) + -7i * (-5 + 7i + x) + x(-5 + 7i + x)) = 0 ((25 + -35i + -5x) + -7i * (-5 + 7i + x) + x(-5 + 7i + x)) = 0 (25 + -35i + -5x + (-5 * -7i + 7i * -7i + x * -7i) + x(-5 + 7i + x)) = 0 Reorder the terms: (25 + -35i + -5x + (35i + -7ix + -49i2) + x(-5 + 7i + x)) = 0 (25 + -35i + -5x + (35i + -7ix + -49i2) + x(-5 + 7i + x)) = 0 (25 + -35i + -5x + 35i + -7ix + -49i2 + (-5 * x + 7i * x + x * x)) = 0 Reorder the terms: (25 + -35i + -5x + 35i + -7ix + -49i2 + (7ix + -5x + x2)) = 0 (25 + -35i + -5x + 35i + -7ix + -49i2 + (7ix + -5x + x2)) = 0 Reorder the terms: (25 + -35i + 35i + -7ix + 7ix + -49i2 + -5x + -5x + x2) = 0 Combine like terms: -35i + 35i = 0 (25 + 0 + -7ix + 7ix + -49i2 + -5x + -5x + x2) = 0 (25 + -7ix + 7ix + -49i2 + -5x + -5x + x2) = 0 Combine like terms: -7ix + 7ix = 0 (25 + 0 + -49i2 + -5x + -5x + x2) = 0 (25 + -49i2 + -5x + -5x + x2) = 0 Combine like terms: -5x + -5x = -10x (25 + -49i2 + -10x + x2) = 0 Solving 25 + -49i2 + -10x + x2 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -49i2 + -10x + -25 + x2 = 0 + -25 Reorder the terms: 25 + -25 + -49i2 + -10x + x2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -49i2 + -10x + x2 = 0 + -25 -49i2 + -10x + x2 = 0 + -25 Combine like terms: 0 + -25 = -25 -49i2 + -10x + x2 = -25 Add '10x' to each side of the equation. -49i2 + -10x + 10x + x2 = -25 + 10x Combine like terms: -10x + 10x = 0 -49i2 + 0 + x2 = -25 + 10x -49i2 + x2 = -25 + 10x Add '-1x2' to each side of the equation. -49i2 + x2 + -1x2 = -25 + 10x + -1x2 Combine like terms: x2 + -1x2 = 0 -49i2 + 0 = -25 + 10x + -1x2 -49i2 = -25 + 10x + -1x2 Divide each side by '-49'. i2 = 0.5102040816 + -0.2040816327x + 0.02040816327x2 Simplifying i2 = 0.5102040816 + -0.2040816327x + 0.02040816327x2 Reorder the terms: -0.5102040816 + i2 + 0.2040816327x + -0.02040816327x2 = 0.5102040816 + -0.2040816327x + 0.02040816327x2 + -0.5102040816 + 0.2040816327x + -0.02040816327x2 Reorder the terms: -0.5102040816 + i2 + 0.2040816327x + -0.02040816327x2 = 0.5102040816 + -0.5102040816 + -0.2040816327x + 0.2040816327x + 0.02040816327x2 + -0.02040816327x2 Combine like terms: 0.5102040816 + -0.5102040816 = 0.0000000000 -0.5102040816 + i2 + 0.2040816327x + -0.02040816327x2 = 0.0000000000 + -0.2040816327x + 0.2040816327x + 0.02040816327x2 + -0.02040816327x2 -0.5102040816 + i2 + 0.2040816327x + -0.02040816327x2 = -0.2040816327x + 0.2040816327x + 0.02040816327x2 + -0.02040816327x2 Combine like terms: -0.2040816327x + 0.2040816327x = 0.0000000000 -0.5102040816 + i2 + 0.2040816327x + -0.02040816327x2 = 0.0000000000 + 0.02040816327x2 + -0.02040816327x2 -0.5102040816 + i2 + 0.2040816327x + -0.02040816327x2 = 0.02040816327x2 + -0.02040816327x2 Combine like terms: 0.02040816327x2 + -0.02040816327x2 = 0.00000000000 -0.5102040816 + i2 + 0.2040816327x + -0.02040816327x2 = 0.00000000000 The solution to this equation could not be determined.
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