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Simplifying (x + -1(-4 + -5i))(x + -1(-4 + 5i)) = 0 (x + (-4 * -1 + -5i * -1))(x + -1(-4 + 5i)) = 0 (x + (4 + 5i))(x + -1(-4 + 5i)) = 0 Reorder the terms: (4 + 5i + x)(x + -1(-4 + 5i)) = 0 (4 + 5i + x)(x + (-4 * -1 + 5i * -1)) = 0 (4 + 5i + x)(x + (4 + -5i)) = 0 Reorder the terms: (4 + 5i + x)(4 + -5i + x) = 0 Multiply (4 + 5i + x) * (4 + -5i + x) (4(4 + -5i + x) + 5i * (4 + -5i + x) + x(4 + -5i + x)) = 0 ((4 * 4 + -5i * 4 + x * 4) + 5i * (4 + -5i + x) + x(4 + -5i + x)) = 0 ((16 + -20i + 4x) + 5i * (4 + -5i + x) + x(4 + -5i + x)) = 0 (16 + -20i + 4x + (4 * 5i + -5i * 5i + x * 5i) + x(4 + -5i + x)) = 0 Reorder the terms: (16 + -20i + 4x + (20i + 5ix + -25i2) + x(4 + -5i + x)) = 0 (16 + -20i + 4x + (20i + 5ix + -25i2) + x(4 + -5i + x)) = 0 (16 + -20i + 4x + 20i + 5ix + -25i2 + (4 * x + -5i * x + x * x)) = 0 Reorder the terms: (16 + -20i + 4x + 20i + 5ix + -25i2 + (-5ix + 4x + x2)) = 0 (16 + -20i + 4x + 20i + 5ix + -25i2 + (-5ix + 4x + x2)) = 0 Reorder the terms: (16 + -20i + 20i + 5ix + -5ix + -25i2 + 4x + 4x + x2) = 0 Combine like terms: -20i + 20i = 0 (16 + 0 + 5ix + -5ix + -25i2 + 4x + 4x + x2) = 0 (16 + 5ix + -5ix + -25i2 + 4x + 4x + x2) = 0 Combine like terms: 5ix + -5ix = 0 (16 + 0 + -25i2 + 4x + 4x + x2) = 0 (16 + -25i2 + 4x + 4x + x2) = 0 Combine like terms: 4x + 4x = 8x (16 + -25i2 + 8x + x2) = 0 Solving 16 + -25i2 + 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 + -25i2 + 8x + -16 + x2 = 0 + -16 Reorder the terms: 16 + -16 + -25i2 + 8x + x2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -25i2 + 8x + x2 = 0 + -16 -25i2 + 8x + x2 = 0 + -16 Combine like terms: 0 + -16 = -16 -25i2 + 8x + x2 = -16 Add '-8x' to each side of the equation. -25i2 + 8x + -8x + x2 = -16 + -8x Combine like terms: 8x + -8x = 0 -25i2 + 0 + x2 = -16 + -8x -25i2 + x2 = -16 + -8x Add '-1x2' to each side of the equation. -25i2 + x2 + -1x2 = -16 + -8x + -1x2 Combine like terms: x2 + -1x2 = 0 -25i2 + 0 = -16 + -8x + -1x2 -25i2 = -16 + -8x + -1x2 Divide each side by '-25'. i2 = 0.64 + 0.32x + 0.04x2 Simplifying i2 = 0.64 + 0.32x + 0.04x2 Reorder the terms: -0.64 + i2 + -0.32x + -0.04x2 = 0.64 + 0.32x + 0.04x2 + -0.64 + -0.32x + -0.04x2 Reorder the terms: -0.64 + i2 + -0.32x + -0.04x2 = 0.64 + -0.64 + 0.32x + -0.32x + 0.04x2 + -0.04x2 Combine like terms: 0.64 + -0.64 = 0.00 -0.64 + i2 + -0.32x + -0.04x2 = 0.00 + 0.32x + -0.32x + 0.04x2 + -0.04x2 -0.64 + i2 + -0.32x + -0.04x2 = 0.32x + -0.32x + 0.04x2 + -0.04x2 Combine like terms: 0.32x + -0.32x = 0.00 -0.64 + i2 + -0.32x + -0.04x2 = 0.00 + 0.04x2 + -0.04x2 -0.64 + i2 + -0.32x + -0.04x2 = 0.04x2 + -0.04x2 Combine like terms: 0.04x2 + -0.04x2 = 0.00 -0.64 + i2 + -0.32x + -0.04x2 = 0.00 The solution to this equation could not be determined.
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