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Simplifying (x + -5)(x + -5)(x + -3i)(x + 3i) = 0 Reorder the terms: (-5 + x)(x + -5)(x + -3i)(x + 3i) = 0 Reorder the terms: (-5 + x)(-5 + x)(x + -3i)(x + 3i) = 0 Reorder the terms: (-5 + x)(-5 + x)(-3i + x)(x + 3i) = 0 Reorder the terms: (-5 + x)(-5 + x)(-3i + x)(3i + x) = 0 Multiply (-5 + x) * (-5 + x) (-5(-5 + x) + x(-5 + x))(-3i + x)(3i + x) = 0 ((-5 * -5 + x * -5) + x(-5 + x))(-3i + x)(3i + x) = 0 ((25 + -5x) + x(-5 + x))(-3i + x)(3i + x) = 0 (25 + -5x + (-5 * x + x * x))(-3i + x)(3i + x) = 0 (25 + -5x + (-5x + x2))(-3i + x)(3i + x) = 0 Combine like terms: -5x + -5x = -10x (25 + -10x + x2)(-3i + x)(3i + x) = 0 Multiply (25 + -10x + x2) * (-3i + x) (25(-3i + x) + -10x * (-3i + x) + x2(-3i + x))(3i + x) = 0 ((-3i * 25 + x * 25) + -10x * (-3i + x) + x2(-3i + x))(3i + x) = 0 ((-75i + 25x) + -10x * (-3i + x) + x2(-3i + x))(3i + x) = 0 (-75i + 25x + (-3i * -10x + x * -10x) + x2(-3i + x))(3i + x) = 0 (-75i + 25x + (30ix + -10x2) + x2(-3i + x))(3i + x) = 0 (-75i + 25x + 30ix + -10x2 + (-3i * x2 + x * x2))(3i + x) = 0 (-75i + 25x + 30ix + -10x2 + (-3ix2 + x3))(3i + x) = 0 Reorder the terms: (-75i + 30ix + -3ix2 + 25x + -10x2 + x3)(3i + x) = 0 (-75i + 30ix + -3ix2 + 25x + -10x2 + x3)(3i + x) = 0 Multiply (-75i + 30ix + -3ix2 + 25x + -10x2 + x3) * (3i + x) (-75i * (3i + x) + 30ix * (3i + x) + -3ix2 * (3i + x) + 25x * (3i + x) + -10x2 * (3i + x) + x3(3i + x)) = 0 ((3i * -75i + x * -75i) + 30ix * (3i + x) + -3ix2 * (3i + x) + 25x * (3i + x) + -10x2 * (3i + x) + x3(3i + x)) = 0 Reorder the terms: ((-75ix + -225i2) + 30ix * (3i + x) + -3ix2 * (3i + x) + 25x * (3i + x) + -10x2 * (3i + x) + x3(3i + x)) = 0 ((-75ix + -225i2) + 30ix * (3i + x) + -3ix2 * (3i + x) + 25x * (3i + x) + -10x2 * (3i + x) + x3(3i + x)) = 0 (-75ix + -225i2 + (3i * 30ix + x * 30ix) + -3ix2 * (3i + x) + 25x * (3i + x) + -10x2 * (3i + x) + x3(3i + x)) = 0 Reorder the terms: (-75ix + -225i2 + (30ix2 + 90i2x) + -3ix2 * (3i + x) + 25x * (3i + x) + -10x2 * (3i + x) + x3(3i + x)) = 0 (-75ix + -225i2 + (30ix2 + 90i2x) + -3ix2 * (3i + x) + 25x * (3i + x) + -10x2 * (3i + x) + x3(3i + x)) = 0 (-75ix + -225i2 + 30ix2 + 90i2x + (3i * -3ix2 + x * -3ix2) + 25x * (3i + x) + -10x2 * (3i + x) + x3(3i + x)) = 0 Reorder the terms: (-75ix + -225i2 + 30ix2 + 90i2x + (-3ix3 + -9i2x2) + 25x * (3i + x) + -10x2 * (3i + x) + x3(3i + x)) = 0 (-75ix + -225i2 + 30ix2 + 90i2x + (-3ix3 + -9i2x2) + 25x * (3i + x) + -10x2 * (3i + x) + x3(3i + x)) = 0 (-75ix + -225i2 + 30ix2 + 90i2x + -3ix3 + -9i2x2 + (3i * 25x + x * 25x) + -10x2 * (3i + x) + x3(3i + x)) = 0 (-75ix + -225i2 + 30ix2 + 90i2x + -3ix3 + -9i2x2 + (75ix + 25x2) + -10x2 * (3i + x) + x3(3i + x)) = 0 (-75ix + -225i2 + 30ix2 + 90i2x + -3ix3 + -9i2x2 + 75ix + 25x2 + (3i * -10x2 + x * -10x2) + x3(3i + x)) = 0 (-75ix + -225i2 + 30ix2 + 90i2x + -3ix3 + -9i2x2 + 75ix + 25x2 + (-30ix2 + -10x3) + x3(3i + x)) = 0 (-75ix + -225i2 + 30ix2 + 90i2x + -3ix3 + -9i2x2 + 75ix + 25x2 + -30ix2 + -10x3 + (3i * x3 + x * x3)) = 0 (-75ix + -225i2 + 30ix2 + 90i2x + -3ix3 + -9i2x2 + 75ix + 25x2 + -30ix2 + -10x3 + (3ix3 + x4)) = 0 Reorder the terms: (-75ix + 75ix + 30ix2 + -30ix2 + -3ix3 + 3ix3 + -225i2 + 90i2x + -9i2x2 + 25x2 + -10x3 + x4) = 0 Combine like terms: -75ix + 75ix = 0 (0 + 30ix2 + -30ix2 + -3ix3 + 3ix3 + -225i2 + 90i2x + -9i2x2 + 25x2 + -10x3 + x4) = 0 (30ix2 + -30ix2 + -3ix3 + 3ix3 + -225i2 + 90i2x + -9i2x2 + 25x2 + -10x3 + x4) = 0 Combine like terms: 30ix2 + -30ix2 = 0 (0 + -3ix3 + 3ix3 + -225i2 + 90i2x + -9i2x2 + 25x2 + -10x3 + x4) = 0 (-3ix3 + 3ix3 + -225i2 + 90i2x + -9i2x2 + 25x2 + -10x3 + x4) = 0 Combine like terms: -3ix3 + 3ix3 = 0 (0 + -225i2 + 90i2x + -9i2x2 + 25x2 + -10x3 + x4) = 0 (-225i2 + 90i2x + -9i2x2 + 25x2 + -10x3 + x4) = 0 Solving -225i2 + 90i2x + -9i2x2 + 25x2 + -10x3 + x4 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-25x2' to each side of the equation. -225i2 + 90i2x + -9i2x2 + 25x2 + -10x3 + -25x2 + x4 = 0 + -25x2 Reorder the terms: -225i2 + 90i2x + -9i2x2 + 25x2 + -25x2 + -10x3 + x4 = 0 + -25x2 Combine like terms: 25x2 + -25x2 = 0 -225i2 + 90i2x + -9i2x2 + 0 + -10x3 + x4 = 0 + -25x2 -225i2 + 90i2x + -9i2x2 + -10x3 + x4 = 0 + -25x2 Remove the zero: -225i2 + 90i2x + -9i2x2 + -10x3 + x4 = -25x2 Add '10x3' to each side of the equation. -225i2 + 90i2x + -9i2x2 + -10x3 + 10x3 + x4 = -25x2 + 10x3 Combine like terms: -10x3 + 10x3 = 0 -225i2 + 90i2x + -9i2x2 + 0 + x4 = -25x2 + 10x3 -225i2 + 90i2x + -9i2x2 + x4 = -25x2 + 10x3 Add '-1x4' to each side of the equation. -225i2 + 90i2x + -9i2x2 + x4 + -1x4 = -25x2 + 10x3 + -1x4 Combine like terms: x4 + -1x4 = 0 -225i2 + 90i2x + -9i2x2 + 0 = -25x2 + 10x3 + -1x4 -225i2 + 90i2x + -9i2x2 = -25x2 + 10x3 + -1x4 Reorder the terms: -225i2 + 90i2x + -9i2x2 + 25x2 + -10x3 + x4 = -25x2 + 25x2 + 10x3 + -10x3 + -1x4 + x4 Combine like terms: -25x2 + 25x2 = 0 -225i2 + 90i2x + -9i2x2 + 25x2 + -10x3 + x4 = 0 + 10x3 + -10x3 + -1x4 + x4 -225i2 + 90i2x + -9i2x2 + 25x2 + -10x3 + x4 = 10x3 + -10x3 + -1x4 + x4 Combine like terms: 10x3 + -10x3 = 0 -225i2 + 90i2x + -9i2x2 + 25x2 + -10x3 + x4 = 0 + -1x4 + x4 -225i2 + 90i2x + -9i2x2 + 25x2 + -10x3 + x4 = -1x4 + x4 Combine like terms: -1x4 + x4 = 0 -225i2 + 90i2x + -9i2x2 + 25x2 + -10x3 + x4 = 0 The solution to this equation could not be determined.
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