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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 = 3x (-4 + 3x + x2)(5i + x)(-5i + x) = 0 Multiply (-4 + 3x + x2) * (5i + x) (-4(5i + x) + 3x * (5i + x) + x2(5i + x))(-5i + x) = 0 ((5i * -4 + x * -4) + 3x * (5i + x) + x2(5i + x))(-5i + x) = 0 ((-20i + -4x) + 3x * (5i + x) + x2(5i + x))(-5i + x) = 0 (-20i + -4x + (5i * 3x + x * 3x) + x2(5i + x))(-5i + x) = 0 (-20i + -4x + (15ix + 3x2) + x2(5i + x))(-5i + x) = 0 (-20i + -4x + 15ix + 3x2 + (5i * x2 + x * x2))(-5i + x) = 0 (-20i + -4x + 15ix + 3x2 + (5ix2 + x3))(-5i + x) = 0 Reorder the terms: (-20i + 15ix + 5ix2 + -4x + 3x2 + x3)(-5i + x) = 0 (-20i + 15ix + 5ix2 + -4x + 3x2 + x3)(-5i + x) = 0 Multiply (-20i + 15ix + 5ix2 + -4x + 3x2 + x3) * (-5i + x) (-20i * (-5i + x) + 15ix * (-5i + x) + 5ix2 * (-5i + x) + -4x * (-5i + x) + 3x2 * (-5i + x) + x3(-5i + x)) = 0 ((-5i * -20i + x * -20i) + 15ix * (-5i + x) + 5ix2 * (-5i + x) + -4x * (-5i + x) + 3x2 * (-5i + x) + x3(-5i + x)) = 0 Reorder the terms: ((-20ix + 100i2) + 15ix * (-5i + x) + 5ix2 * (-5i + x) + -4x * (-5i + x) + 3x2 * (-5i + x) + x3(-5i + x)) = 0 ((-20ix + 100i2) + 15ix * (-5i + x) + 5ix2 * (-5i + x) + -4x * (-5i + x) + 3x2 * (-5i + x) + x3(-5i + x)) = 0 (-20ix + 100i2 + (-5i * 15ix + x * 15ix) + 5ix2 * (-5i + x) + -4x * (-5i + x) + 3x2 * (-5i + x) + x3(-5i + x)) = 0 Reorder the terms: (-20ix + 100i2 + (15ix2 + -75i2x) + 5ix2 * (-5i + x) + -4x * (-5i + x) + 3x2 * (-5i + x) + x3(-5i + x)) = 0 (-20ix + 100i2 + (15ix2 + -75i2x) + 5ix2 * (-5i + x) + -4x * (-5i + x) + 3x2 * (-5i + x) + x3(-5i + x)) = 0 (-20ix + 100i2 + 15ix2 + -75i2x + (-5i * 5ix2 + x * 5ix2) + -4x * (-5i + x) + 3x2 * (-5i + x) + x3(-5i + x)) = 0 Reorder the terms: (-20ix + 100i2 + 15ix2 + -75i2x + (5ix3 + -25i2x2) + -4x * (-5i + x) + 3x2 * (-5i + x) + x3(-5i + x)) = 0 (-20ix + 100i2 + 15ix2 + -75i2x + (5ix3 + -25i2x2) + -4x * (-5i + x) + 3x2 * (-5i + x) + x3(-5i + x)) = 0 (-20ix + 100i2 + 15ix2 + -75i2x + 5ix3 + -25i2x2 + (-5i * -4x + x * -4x) + 3x2 * (-5i + x) + x3(-5i + x)) = 0 (-20ix + 100i2 + 15ix2 + -75i2x + 5ix3 + -25i2x2 + (20ix + -4x2) + 3x2 * (-5i + x) + x3(-5i + x)) = 0 (-20ix + 100i2 + 15ix2 + -75i2x + 5ix3 + -25i2x2 + 20ix + -4x2 + (-5i * 3x2 + x * 3x2) + x3(-5i + x)) = 0 (-20ix + 100i2 + 15ix2 + -75i2x + 5ix3 + -25i2x2 + 20ix + -4x2 + (-15ix2 + 3x3) + x3(-5i + x)) = 0 (-20ix + 100i2 + 15ix2 + -75i2x + 5ix3 + -25i2x2 + 20ix + -4x2 + -15ix2 + 3x3 + (-5i * x3 + x * x3)) = 0 (-20ix + 100i2 + 15ix2 + -75i2x + 5ix3 + -25i2x2 + 20ix + -4x2 + -15ix2 + 3x3 + (-5ix3 + x4)) = 0 Reorder the terms: (-20ix + 20ix + 15ix2 + -15ix2 + 5ix3 + -5ix3 + 100i2 + -75i2x + -25i2x2 + -4x2 + 3x3 + x4) = 0 Combine like terms: -20ix + 20ix = 0 (0 + 15ix2 + -15ix2 + 5ix3 + -5ix3 + 100i2 + -75i2x + -25i2x2 + -4x2 + 3x3 + x4) = 0 (15ix2 + -15ix2 + 5ix3 + -5ix3 + 100i2 + -75i2x + -25i2x2 + -4x2 + 3x3 + x4) = 0 Combine like terms: 15ix2 + -15ix2 = 0 (0 + 5ix3 + -5ix3 + 100i2 + -75i2x + -25i2x2 + -4x2 + 3x3 + x4) = 0 (5ix3 + -5ix3 + 100i2 + -75i2x + -25i2x2 + -4x2 + 3x3 + x4) = 0 Combine like terms: 5ix3 + -5ix3 = 0 (0 + 100i2 + -75i2x + -25i2x2 + -4x2 + 3x3 + x4) = 0 (100i2 + -75i2x + -25i2x2 + -4x2 + 3x3 + x4) = 0 Solving 100i2 + -75i2x + -25i2x2 + -4x2 + 3x3 + 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 + -75i2x + -25i2x2 + -4x2 + 3x3 + 4x2 + x4 = 0 + 4x2 Reorder the terms: 100i2 + -75i2x + -25i2x2 + -4x2 + 4x2 + 3x3 + x4 = 0 + 4x2 Combine like terms: -4x2 + 4x2 = 0 100i2 + -75i2x + -25i2x2 + 0 + 3x3 + x4 = 0 + 4x2 100i2 + -75i2x + -25i2x2 + 3x3 + x4 = 0 + 4x2 Remove the zero: 100i2 + -75i2x + -25i2x2 + 3x3 + x4 = 4x2 Add '-3x3' to each side of the equation. 100i2 + -75i2x + -25i2x2 + 3x3 + -3x3 + x4 = 4x2 + -3x3 Combine like terms: 3x3 + -3x3 = 0 100i2 + -75i2x + -25i2x2 + 0 + x4 = 4x2 + -3x3 100i2 + -75i2x + -25i2x2 + x4 = 4x2 + -3x3 Add '-1x4' to each side of the equation. 100i2 + -75i2x + -25i2x2 + x4 + -1x4 = 4x2 + -3x3 + -1x4 Combine like terms: x4 + -1x4 = 0 100i2 + -75i2x + -25i2x2 + 0 = 4x2 + -3x3 + -1x4 100i2 + -75i2x + -25i2x2 = 4x2 + -3x3 + -1x4 Reorder the terms: 100i2 + -75i2x + -25i2x2 + -4x2 + 3x3 + x4 = 4x2 + -4x2 + -3x3 + 3x3 + -1x4 + x4 Combine like terms: 4x2 + -4x2 = 0 100i2 + -75i2x + -25i2x2 + -4x2 + 3x3 + x4 = 0 + -3x3 + 3x3 + -1x4 + x4 100i2 + -75i2x + -25i2x2 + -4x2 + 3x3 + x4 = -3x3 + 3x3 + -1x4 + x4 Combine like terms: -3x3 + 3x3 = 0 100i2 + -75i2x + -25i2x2 + -4x2 + 3x3 + x4 = 0 + -1x4 + x4 100i2 + -75i2x + -25i2x2 + -4x2 + 3x3 + x4 = -1x4 + x4 Combine like terms: -1x4 + x4 = 0 100i2 + -75i2x + -25i2x2 + -4x2 + 3x3 + x4 = 0 The solution to this equation could not be determined.
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