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Simplifying (x + -1(4 + 7i))(x + -1(4 + -7i)) = 0 (x + (4 * -1 + 7i * -1))(x + -1(4 + -7i)) = 0 (x + (-4 + -7i))(x + -1(4 + -7i)) = 0 Reorder the terms: (-4 + -7i + x)(x + -1(4 + -7i)) = 0 (-4 + -7i + x)(x + (4 * -1 + -7i * -1)) = 0 (-4 + -7i + x)(x + (-4 + 7i)) = 0 Reorder the terms: (-4 + -7i + x)(-4 + 7i + x) = 0 Multiply (-4 + -7i + x) * (-4 + 7i + x) (-4(-4 + 7i + x) + -7i * (-4 + 7i + x) + x(-4 + 7i + x)) = 0 ((-4 * -4 + 7i * -4 + x * -4) + -7i * (-4 + 7i + x) + x(-4 + 7i + x)) = 0 ((16 + -28i + -4x) + -7i * (-4 + 7i + x) + x(-4 + 7i + x)) = 0 (16 + -28i + -4x + (-4 * -7i + 7i * -7i + x * -7i) + x(-4 + 7i + x)) = 0 Reorder the terms: (16 + -28i + -4x + (28i + -7ix + -49i2) + x(-4 + 7i + x)) = 0 (16 + -28i + -4x + (28i + -7ix + -49i2) + x(-4 + 7i + x)) = 0 (16 + -28i + -4x + 28i + -7ix + -49i2 + (-4 * x + 7i * x + x * x)) = 0 Reorder the terms: (16 + -28i + -4x + 28i + -7ix + -49i2 + (7ix + -4x + x2)) = 0 (16 + -28i + -4x + 28i + -7ix + -49i2 + (7ix + -4x + x2)) = 0 Reorder the terms: (16 + -28i + 28i + -7ix + 7ix + -49i2 + -4x + -4x + x2) = 0 Combine like terms: -28i + 28i = 0 (16 + 0 + -7ix + 7ix + -49i2 + -4x + -4x + x2) = 0 (16 + -7ix + 7ix + -49i2 + -4x + -4x + x2) = 0 Combine like terms: -7ix + 7ix = 0 (16 + 0 + -49i2 + -4x + -4x + x2) = 0 (16 + -49i2 + -4x + -4x + x2) = 0 Combine like terms: -4x + -4x = -8x (16 + -49i2 + -8x + x2) = 0 Solving 16 + -49i2 + -8x + x2 = 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 + -49i2 + -8x + -16 + x2 = 0 + -16 Reorder the terms: 16 + -16 + -49i2 + -8x + x2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -49i2 + -8x + x2 = 0 + -16 -49i2 + -8x + x2 = 0 + -16 Combine like terms: 0 + -16 = -16 -49i2 + -8x + x2 = -16 Add '8x' to each side of the equation. -49i2 + -8x + 8x + x2 = -16 + 8x Combine like terms: -8x + 8x = 0 -49i2 + 0 + x2 = -16 + 8x -49i2 + x2 = -16 + 8x Add '-1x2' to each side of the equation. -49i2 + x2 + -1x2 = -16 + 8x + -1x2 Combine like terms: x2 + -1x2 = 0 -49i2 + 0 = -16 + 8x + -1x2 -49i2 = -16 + 8x + -1x2 Divide each side by '-49'. i2 = 0.3265306122 + -0.1632653061x + 0.02040816327x2 Simplifying i2 = 0.3265306122 + -0.1632653061x + 0.02040816327x2 Reorder the terms: -0.3265306122 + i2 + 0.1632653061x + -0.02040816327x2 = 0.3265306122 + -0.1632653061x + 0.02040816327x2 + -0.3265306122 + 0.1632653061x + -0.02040816327x2 Reorder the terms: -0.3265306122 + i2 + 0.1632653061x + -0.02040816327x2 = 0.3265306122 + -0.3265306122 + -0.1632653061x + 0.1632653061x + 0.02040816327x2 + -0.02040816327x2 Combine like terms: 0.3265306122 + -0.3265306122 = 0.0000000000 -0.3265306122 + i2 + 0.1632653061x + -0.02040816327x2 = 0.0000000000 + -0.1632653061x + 0.1632653061x + 0.02040816327x2 + -0.02040816327x2 -0.3265306122 + i2 + 0.1632653061x + -0.02040816327x2 = -0.1632653061x + 0.1632653061x + 0.02040816327x2 + -0.02040816327x2 Combine like terms: -0.1632653061x + 0.1632653061x = 0.0000000000 -0.3265306122 + i2 + 0.1632653061x + -0.02040816327x2 = 0.0000000000 + 0.02040816327x2 + -0.02040816327x2 -0.3265306122 + i2 + 0.1632653061x + -0.02040816327x2 = 0.02040816327x2 + -0.02040816327x2 Combine like terms: 0.02040816327x2 + -0.02040816327x2 = 0.00000000000 -0.3265306122 + i2 + 0.1632653061x + -0.02040816327x2 = 0.00000000000 The solution to this equation could not be determined.
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