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Simplifying (x + -1(5 + -5i))(x + -1(5 + 5i)) = 0 (x + (5 * -1 + -5i * -1))(x + -1(5 + 5i)) = 0 (x + (-5 + 5i))(x + -1(5 + 5i)) = 0 Reorder the terms: (-5 + 5i + x)(x + -1(5 + 5i)) = 0 (-5 + 5i + x)(x + (5 * -1 + 5i * -1)) = 0 (-5 + 5i + x)(x + (-5 + -5i)) = 0 Reorder the terms: (-5 + 5i + x)(-5 + -5i + x) = 0 Multiply (-5 + 5i + x) * (-5 + -5i + x) (-5(-5 + -5i + x) + 5i * (-5 + -5i + x) + x(-5 + -5i + x)) = 0 ((-5 * -5 + -5i * -5 + x * -5) + 5i * (-5 + -5i + x) + x(-5 + -5i + x)) = 0 ((25 + 25i + -5x) + 5i * (-5 + -5i + x) + x(-5 + -5i + x)) = 0 (25 + 25i + -5x + (-5 * 5i + -5i * 5i + x * 5i) + x(-5 + -5i + x)) = 0 Reorder the terms: (25 + 25i + -5x + (-25i + 5ix + -25i2) + x(-5 + -5i + x)) = 0 (25 + 25i + -5x + (-25i + 5ix + -25i2) + x(-5 + -5i + x)) = 0 (25 + 25i + -5x + -25i + 5ix + -25i2 + (-5 * x + -5i * x + x * x)) = 0 Reorder the terms: (25 + 25i + -5x + -25i + 5ix + -25i2 + (-5ix + -5x + x2)) = 0 (25 + 25i + -5x + -25i + 5ix + -25i2 + (-5ix + -5x + x2)) = 0 Reorder the terms: (25 + 25i + -25i + 5ix + -5ix + -25i2 + -5x + -5x + x2) = 0 Combine like terms: 25i + -25i = 0 (25 + 0 + 5ix + -5ix + -25i2 + -5x + -5x + x2) = 0 (25 + 5ix + -5ix + -25i2 + -5x + -5x + x2) = 0 Combine like terms: 5ix + -5ix = 0 (25 + 0 + -25i2 + -5x + -5x + x2) = 0 (25 + -25i2 + -5x + -5x + x2) = 0 Combine like terms: -5x + -5x = -10x (25 + -25i2 + -10x + x2) = 0 Solving 25 + -25i2 + -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 + -25i2 + -10x + -25 + x2 = 0 + -25 Reorder the terms: 25 + -25 + -25i2 + -10x + x2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -25i2 + -10x + x2 = 0 + -25 -25i2 + -10x + x2 = 0 + -25 Combine like terms: 0 + -25 = -25 -25i2 + -10x + x2 = -25 Add '10x' to each side of the equation. -25i2 + -10x + 10x + x2 = -25 + 10x Combine like terms: -10x + 10x = 0 -25i2 + 0 + x2 = -25 + 10x -25i2 + x2 = -25 + 10x Add '-1x2' to each side of the equation. -25i2 + x2 + -1x2 = -25 + 10x + -1x2 Combine like terms: x2 + -1x2 = 0 -25i2 + 0 = -25 + 10x + -1x2 -25i2 = -25 + 10x + -1x2 Divide each side by '-25'. i2 = 1 + -0.4x + 0.04x2 Simplifying i2 = 1 + -0.4x + 0.04x2 Reorder the terms: -1 + i2 + 0.4x + -0.04x2 = 1 + -0.4x + 0.04x2 + -1 + 0.4x + -0.04x2 Reorder the terms: -1 + i2 + 0.4x + -0.04x2 = 1 + -1 + -0.4x + 0.4x + 0.04x2 + -0.04x2 Combine like terms: 1 + -1 = 0 -1 + i2 + 0.4x + -0.04x2 = 0 + -0.4x + 0.4x + 0.04x2 + -0.04x2 -1 + i2 + 0.4x + -0.04x2 = -0.4x + 0.4x + 0.04x2 + -0.04x2 Combine like terms: -0.4x + 0.4x = 0.0 -1 + i2 + 0.4x + -0.04x2 = 0.0 + 0.04x2 + -0.04x2 -1 + i2 + 0.4x + -0.04x2 = 0.04x2 + -0.04x2 Combine like terms: 0.04x2 + -0.04x2 = 0.00 -1 + i2 + 0.4x + -0.04x2 = 0.00 The solution to this equation could not be determined.
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