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Simplifying (x + -1)(x + -4)(x + 5i)(x + -5i) = 0 Reorder the terms: (-1 + x)(x + -4)(x + 5i)(x + -5i) = 0 Reorder the terms: (-1 + x)(-4 + x)(x + 5i)(x + -5i) = 0 Reorder the terms: (-1 + x)(-4 + x)(5i + x)(x + -5i) = 0 Reorder the terms: (-1 + x)(-4 + x)(5i + x)(-5i + x) = 0 Multiply (-1 + x) * (-4 + x) (-1(-4 + x) + x(-4 + x))(5i + x)(-5i + x) = 0 ((-4 * -1 + x * -1) + x(-4 + x))(5i + x)(-5i + x) = 0 ((4 + -1x) + x(-4 + x))(5i + x)(-5i + x) = 0 (4 + -1x + (-4 * x + x * x))(5i + x)(-5i + x) = 0 (4 + -1x + (-4x + x2))(5i + x)(-5i + x) = 0 Combine like terms: -1x + -4x = -5x (4 + -5x + x2)(5i + x)(-5i + x) = 0 Multiply (4 + -5x + x2) * (5i + x) (4(5i + x) + -5x * (5i + x) + x2(5i + x))(-5i + x) = 0 ((5i * 4 + x * 4) + -5x * (5i + x) + x2(5i + x))(-5i + x) = 0 ((20i + 4x) + -5x * (5i + x) + x2(5i + x))(-5i + x) = 0 (20i + 4x + (5i * -5x + x * -5x) + x2(5i + x))(-5i + x) = 0 (20i + 4x + (-25ix + -5x2) + x2(5i + x))(-5i + x) = 0 (20i + 4x + -25ix + -5x2 + (5i * x2 + x * x2))(-5i + x) = 0 (20i + 4x + -25ix + -5x2 + (5ix2 + x3))(-5i + x) = 0 Reorder the terms: (20i + -25ix + 5ix2 + 4x + -5x2 + x3)(-5i + x) = 0 (20i + -25ix + 5ix2 + 4x + -5x2 + x3)(-5i + x) = 0 Multiply (20i + -25ix + 5ix2 + 4x + -5x2 + x3) * (-5i + x) (20i * (-5i + x) + -25ix * (-5i + x) + 5ix2 * (-5i + x) + 4x * (-5i + x) + -5x2 * (-5i + x) + x3(-5i + x)) = 0 ((-5i * 20i + x * 20i) + -25ix * (-5i + x) + 5ix2 * (-5i + x) + 4x * (-5i + x) + -5x2 * (-5i + x) + x3(-5i + x)) = 0 Reorder the terms: ((20ix + -100i2) + -25ix * (-5i + x) + 5ix2 * (-5i + x) + 4x * (-5i + x) + -5x2 * (-5i + x) + x3(-5i + x)) = 0 ((20ix + -100i2) + -25ix * (-5i + x) + 5ix2 * (-5i + x) + 4x * (-5i + x) + -5x2 * (-5i + x) + x3(-5i + x)) = 0 (20ix + -100i2 + (-5i * -25ix + x * -25ix) + 5ix2 * (-5i + x) + 4x * (-5i + x) + -5x2 * (-5i + x) + x3(-5i + x)) = 0 Reorder the terms: (20ix + -100i2 + (-25ix2 + 125i2x) + 5ix2 * (-5i + x) + 4x * (-5i + x) + -5x2 * (-5i + x) + x3(-5i + x)) = 0 (20ix + -100i2 + (-25ix2 + 125i2x) + 5ix2 * (-5i + x) + 4x * (-5i + x) + -5x2 * (-5i + x) + x3(-5i + x)) = 0 (20ix + -100i2 + -25ix2 + 125i2x + (-5i * 5ix2 + x * 5ix2) + 4x * (-5i + x) + -5x2 * (-5i + x) + x3(-5i + x)) = 0 Reorder the terms: (20ix + -100i2 + -25ix2 + 125i2x + (5ix3 + -25i2x2) + 4x * (-5i + x) + -5x2 * (-5i + x) + x3(-5i + x)) = 0 (20ix + -100i2 + -25ix2 + 125i2x + (5ix3 + -25i2x2) + 4x * (-5i + x) + -5x2 * (-5i + x) + x3(-5i + x)) = 0 (20ix + -100i2 + -25ix2 + 125i2x + 5ix3 + -25i2x2 + (-5i * 4x + x * 4x) + -5x2 * (-5i + x) + x3(-5i + x)) = 0 (20ix + -100i2 + -25ix2 + 125i2x + 5ix3 + -25i2x2 + (-20ix + 4x2) + -5x2 * (-5i + x) + x3(-5i + x)) = 0 (20ix + -100i2 + -25ix2 + 125i2x + 5ix3 + -25i2x2 + -20ix + 4x2 + (-5i * -5x2 + x * -5x2) + x3(-5i + x)) = 0 (20ix + -100i2 + -25ix2 + 125i2x + 5ix3 + -25i2x2 + -20ix + 4x2 + (25ix2 + -5x3) + x3(-5i + x)) = 0 (20ix + -100i2 + -25ix2 + 125i2x + 5ix3 + -25i2x2 + -20ix + 4x2 + 25ix2 + -5x3 + (-5i * x3 + x * x3)) = 0 (20ix + -100i2 + -25ix2 + 125i2x + 5ix3 + -25i2x2 + -20ix + 4x2 + 25ix2 + -5x3 + (-5ix3 + x4)) = 0 Reorder the terms: (20ix + -20ix + -25ix2 + 25ix2 + 5ix3 + -5ix3 + -100i2 + 125i2x + -25i2x2 + 4x2 + -5x3 + x4) = 0 Combine like terms: 20ix + -20ix = 0 (0 + -25ix2 + 25ix2 + 5ix3 + -5ix3 + -100i2 + 125i2x + -25i2x2 + 4x2 + -5x3 + x4) = 0 (-25ix2 + 25ix2 + 5ix3 + -5ix3 + -100i2 + 125i2x + -25i2x2 + 4x2 + -5x3 + x4) = 0 Combine like terms: -25ix2 + 25ix2 = 0 (0 + 5ix3 + -5ix3 + -100i2 + 125i2x + -25i2x2 + 4x2 + -5x3 + x4) = 0 (5ix3 + -5ix3 + -100i2 + 125i2x + -25i2x2 + 4x2 + -5x3 + x4) = 0 Combine like terms: 5ix3 + -5ix3 = 0 (0 + -100i2 + 125i2x + -25i2x2 + 4x2 + -5x3 + x4) = 0 (-100i2 + 125i2x + -25i2x2 + 4x2 + -5x3 + x4) = 0 Solving -100i2 + 125i2x + -25i2x2 + 4x2 + -5x3 + x4 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-4x2' to each side of the equation. -100i2 + 125i2x + -25i2x2 + 4x2 + -5x3 + -4x2 + x4 = 0 + -4x2 Reorder the terms: -100i2 + 125i2x + -25i2x2 + 4x2 + -4x2 + -5x3 + x4 = 0 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -100i2 + 125i2x + -25i2x2 + 0 + -5x3 + x4 = 0 + -4x2 -100i2 + 125i2x + -25i2x2 + -5x3 + x4 = 0 + -4x2 Remove the zero: -100i2 + 125i2x + -25i2x2 + -5x3 + x4 = -4x2 Add '5x3' to each side of the equation. -100i2 + 125i2x + -25i2x2 + -5x3 + 5x3 + x4 = -4x2 + 5x3 Combine like terms: -5x3 + 5x3 = 0 -100i2 + 125i2x + -25i2x2 + 0 + x4 = -4x2 + 5x3 -100i2 + 125i2x + -25i2x2 + x4 = -4x2 + 5x3 Add '-1x4' to each side of the equation. -100i2 + 125i2x + -25i2x2 + x4 + -1x4 = -4x2 + 5x3 + -1x4 Combine like terms: x4 + -1x4 = 0 -100i2 + 125i2x + -25i2x2 + 0 = -4x2 + 5x3 + -1x4 -100i2 + 125i2x + -25i2x2 = -4x2 + 5x3 + -1x4 Reorder the terms: -100i2 + 125i2x + -25i2x2 + 4x2 + -5x3 + x4 = -4x2 + 4x2 + 5x3 + -5x3 + -1x4 + x4 Combine like terms: -4x2 + 4x2 = 0 -100i2 + 125i2x + -25i2x2 + 4x2 + -5x3 + x4 = 0 + 5x3 + -5x3 + -1x4 + x4 -100i2 + 125i2x + -25i2x2 + 4x2 + -5x3 + x4 = 5x3 + -5x3 + -1x4 + x4 Combine like terms: 5x3 + -5x3 = 0 -100i2 + 125i2x + -25i2x2 + 4x2 + -5x3 + x4 = 0 + -1x4 + x4 -100i2 + 125i2x + -25i2x2 + 4x2 + -5x3 + x4 = -1x4 + x4 Combine like terms: -1x4 + x4 = 0 -100i2 + 125i2x + -25i2x2 + 4x2 + -5x3 + x4 = 0 The solution to this equation could not be determined.
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