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Simplifying (x + 5)(x + i)(x + -1i)(-7 + i)(-7 + -1i) = 0 Reorder the terms: (5 + x)(x + i)(x + -1i)(-7 + i)(-7 + -1i) = 0 Reorder the terms: (5 + x)(i + x)(x + -1i)(-7 + i)(-7 + -1i) = 0 Reorder the terms: (5 + x)(i + x)(-1i + x)(-7 + i)(-7 + -1i) = 0 Multiply (5 + x) * (i + x) (5(i + x) + x(i + x))(-1i + x)(-7 + i)(-7 + -1i) = 0 ((i * 5 + x * 5) + x(i + x))(-1i + x)(-7 + i)(-7 + -1i) = 0 ((5i + 5x) + x(i + x))(-1i + x)(-7 + i)(-7 + -1i) = 0 (5i + 5x + (i * x + x * x))(-1i + x)(-7 + i)(-7 + -1i) = 0 (5i + 5x + (ix + x2))(-1i + x)(-7 + i)(-7 + -1i) = 0 Reorder the terms: (5i + ix + 5x + x2)(-1i + x)(-7 + i)(-7 + -1i) = 0 (5i + ix + 5x + x2)(-1i + x)(-7 + i)(-7 + -1i) = 0 Multiply (5i + ix + 5x + x2) * (-1i + x) (5i * (-1i + x) + ix(-1i + x) + 5x * (-1i + x) + x2(-1i + x))(-7 + i)(-7 + -1i) = 0 ((-1i * 5i + x * 5i) + ix(-1i + x) + 5x * (-1i + x) + x2(-1i + x))(-7 + i)(-7 + -1i) = 0 Reorder the terms: ((5ix + -5i2) + ix(-1i + x) + 5x * (-1i + x) + x2(-1i + x))(-7 + i)(-7 + -1i) = 0 ((5ix + -5i2) + ix(-1i + x) + 5x * (-1i + x) + x2(-1i + x))(-7 + i)(-7 + -1i) = 0 (5ix + -5i2 + (-1i * ix + x * ix) + 5x * (-1i + x) + x2(-1i + x))(-7 + i)(-7 + -1i) = 0 Reorder the terms: (5ix + -5i2 + (ix2 + -1i2x) + 5x * (-1i + x) + x2(-1i + x))(-7 + i)(-7 + -1i) = 0 (5ix + -5i2 + (ix2 + -1i2x) + 5x * (-1i + x) + x2(-1i + x))(-7 + i)(-7 + -1i) = 0 (5ix + -5i2 + ix2 + -1i2x + (-1i * 5x + x * 5x) + x2(-1i + x))(-7 + i)(-7 + -1i) = 0 (5ix + -5i2 + ix2 + -1i2x + (-5ix + 5x2) + x2(-1i + x))(-7 + i)(-7 + -1i) = 0 (5ix + -5i2 + ix2 + -1i2x + -5ix + 5x2 + (-1i * x2 + x * x2))(-7 + i)(-7 + -1i) = 0 (5ix + -5i2 + ix2 + -1i2x + -5ix + 5x2 + (-1ix2 + x3))(-7 + i)(-7 + -1i) = 0 Reorder the terms: (5ix + -5ix + ix2 + -1ix2 + -5i2 + -1i2x + 5x2 + x3)(-7 + i)(-7 + -1i) = 0 Combine like terms: 5ix + -5ix = 0 (0 + ix2 + -1ix2 + -5i2 + -1i2x + 5x2 + x3)(-7 + i)(-7 + -1i) = 0 (ix2 + -1ix2 + -5i2 + -1i2x + 5x2 + x3)(-7 + i)(-7 + -1i) = 0 Combine like terms: ix2 + -1ix2 = 0 (0 + -5i2 + -1i2x + 5x2 + x3)(-7 + i)(-7 + -1i) = 0 (-5i2 + -1i2x + 5x2 + x3)(-7 + i)(-7 + -1i) = 0 Multiply (-5i2 + -1i2x + 5x2 + x3) * (-7 + i) (-5i2 * (-7 + i) + -1i2x * (-7 + i) + 5x2 * (-7 + i) + x3(-7 + i))(-7 + -1i) = 0 ((-7 * -5i2 + i * -5i2) + -1i2x * (-7 + i) + 5x2 * (-7 + i) + x3(-7 + i))(-7 + -1i) = 0 ((35i2 + -5i3) + -1i2x * (-7 + i) + 5x2 * (-7 + i) + x3(-7 + i))(-7 + -1i) = 0 (35i2 + -5i3 + (-7 * -1i2x + i * -1i2x) + 5x2 * (-7 + i) + x3(-7 + i))(-7 + -1i) = 0 (35i2 + -5i3 + (7i2x + -1i3x) + 5x2 * (-7 + i) + x3(-7 + i))(-7 + -1i) = 0 (35i2 + -5i3 + 7i2x + -1i3x + (-7 * 5x2 + i * 5x2) + x3(-7 + i))(-7 + -1i) = 0 Reorder the terms: (35i2 + -5i3 + 7i2x + -1i3x + (5ix2 + -35x2) + x3(-7 + i))(-7 + -1i) = 0 (35i2 + -5i3 + 7i2x + -1i3x + (5ix2 + -35x2) + x3(-7 + i))(-7 + -1i) = 0 (35i2 + -5i3 + 7i2x + -1i3x + 5ix2 + -35x2 + (-7 * x3 + i * x3))(-7 + -1i) = 0 Reorder the terms: (35i2 + -5i3 + 7i2x + -1i3x + 5ix2 + -35x2 + (ix3 + -7x3))(-7 + -1i) = 0 (35i2 + -5i3 + 7i2x + -1i3x + 5ix2 + -35x2 + (ix3 + -7x3))(-7 + -1i) = 0 Reorder the terms: (5ix2 + ix3 + 35i2 + 7i2x + -5i3 + -1i3x + -35x2 + -7x3)(-7 + -1i) = 0 (5ix2 + ix3 + 35i2 + 7i2x + -5i3 + -1i3x + -35x2 + -7x3)(-7 + -1i) = 0 Multiply (5ix2 + ix3 + 35i2 + 7i2x + -5i3 + -1i3x + -35x2 + -7x3) * (-7 + -1i) (5ix2 * (-7 + -1i) + ix3(-7 + -1i) + 35i2 * (-7 + -1i) + 7i2x * (-7 + -1i) + -5i3 * (-7 + -1i) + -1i3x * (-7 + -1i) + -35x2 * (-7 + -1i) + -7x3 * (-7 + -1i)) = 0 ((-7 * 5ix2 + -1i * 5ix2) + ix3(-7 + -1i) + 35i2 * (-7 + -1i) + 7i2x * (-7 + -1i) + -5i3 * (-7 + -1i) + -1i3x * (-7 + -1i) + -35x2 * (-7 + -1i) + -7x3 * (-7 + -1i)) = 0 ((-35ix2 + -5i2x2) + ix3(-7 + -1i) + 35i2 * (-7 + -1i) + 7i2x * (-7 + -1i) + -5i3 * (-7 + -1i) + -1i3x * (-7 + -1i) + -35x2 * (-7 + -1i) + -7x3 * (-7 + -1i)) = 0 (-35ix2 + -5i2x2 + (-7 * ix3 + -1i * ix3) + 35i2 * (-7 + -1i) + 7i2x * (-7 + -1i) + -5i3 * (-7 + -1i) + -1i3x * (-7 + -1i) + -35x2 * (-7 + -1i) + -7x3 * (-7 + -1i)) = 0 (-35ix2 + -5i2x2 + (-7ix3 + -1i2x3) + 35i2 * (-7 + -1i) + 7i2x * (-7 + -1i) + -5i3 * (-7 + -1i) + -1i3x * (-7 + -1i) + -35x2 * (-7 + -1i) + -7x3 * (-7 + -1i)) = 0 (-35ix2 + -5i2x2 + -7ix3 + -1i2x3 + (-7 * 35i2 + -1i * 35i2) + 7i2x * (-7 + -1i) + -5i3 * (-7 + -1i) + -1i3x * (-7 + -1i) + -35x2 * (-7 + -1i) + -7x3 * (-7 + -1i)) = 0 (-35ix2 + -5i2x2 + -7ix3 + -1i2x3 + (-245i2 + -35i3) + 7i2x * (-7 + -1i) + -5i3 * (-7 + -1i) + -1i3x * (-7 + -1i) + -35x2 * (-7 + -1i) + -7x3 * (-7 + -1i)) = 0 (-35ix2 + -5i2x2 + -7ix3 + -1i2x3 + -245i2 + -35i3 + (-7 * 7i2x + -1i * 7i2x) + -5i3 * (-7 + -1i) + -1i3x * (-7 + -1i) + -35x2 * (-7 + -1i) + -7x3 * (-7 + -1i)) = 0 (-35ix2 + -5i2x2 + -7ix3 + -1i2x3 + -245i2 + -35i3 + (-49i2x + -7i3x) + -5i3 * (-7 + -1i) + -1i3x * (-7 + -1i) + -35x2 * (-7 + -1i) + -7x3 * (-7 + -1i)) = 0 (-35ix2 + -5i2x2 + -7ix3 + -1i2x3 + -245i2 + -35i3 + -49i2x + -7i3x + (-7 * -5i3 + -1i * -5i3) + -1i3x * (-7 + -1i) + -35x2 * (-7 + -1i) + -7x3 * (-7 + -1i)) = 0 (-35ix2 + -5i2x2 + -7ix3 + -1i2x3 + -245i2 + -35i3 + -49i2x + -7i3x + (35i3 + 5i4) + -1i3x * (-7 + -1i) + -35x2 * (-7 + -1i) + -7x3 * (-7 + -1i)) = 0 (-35ix2 + -5i2x2 + -7ix3 + -1i2x3 + -245i2 + -35i3 + -49i2x + -7i3x + 35i3 + 5i4 + (-7 * -1i3x + -1i * -1i3x) + -35x2 * (-7 + -1i) + -7x3 * (-7 + -1i)) = 0 (-35ix2 + -5i2x2 + -7ix3 + -1i2x3 + -245i2 + -35i3 + -49i2x + -7i3x + 35i3 + 5i4 + (7i3x + 1i4x) + -35x2 * (-7 + -1i) + -7x3 * (-7 + -1i)) = 0 (-35ix2 + -5i2x2 + -7ix3 + -1i2x3 + -245i2 + -35i3 + -49i2x + -7i3x + 35i3 + 5i4 + 7i3x + 1i4x + (-7 * -35x2 + -1i * -35x2) + -7x3 * (-7 + -1i)) = 0 Reorder the terms: (-35ix2 + -5i2x2 + -7ix3 + -1i2x3 + -245i2 + -35i3 + -49i2x + -7i3x + 35i3 + 5i4 + 7i3x + 1i4x + (35ix2 + 245x2) + -7x3 * (-7 + -1i)) = 0 (-35ix2 + -5i2x2 + -7ix3 + -1i2x3 + -245i2 + -35i3 + -49i2x + -7i3x + 35i3 + 5i4 + 7i3x + 1i4x + (35ix2 + 245x2) + -7x3 * (-7 + -1i)) = 0 (-35ix2 + -5i2x2 + -7ix3 + -1i2x3 + -245i2 + -35i3 + -49i2x + -7i3x + 35i3 + 5i4 + 7i3x + 1i4x + 35ix2 + 245x2 + (-7 * -7x3 + -1i * -7x3)) = 0 Reorder the terms: (-35ix2 + -5i2x2 + -7ix3 + -1i2x3 + -245i2 + -35i3 + -49i2x + -7i3x + 35i3 + 5i4 + 7i3x + 1i4x + 35ix2 + 245x2 + (7ix3 + 49x3)) = 0 (-35ix2 + -5i2x2 + -7ix3 + -1i2x3 + -245i2 + -35i3 + -49i2x + -7i3x + 35i3 + 5i4 + 7i3x + 1i4x + 35ix2 + 245x2 + (7ix3 + 49x3)) = 0 Reorder the terms: (-35ix2 + 35ix2 + -7ix3 + 7ix3 + -245i2 + -49i2x + -5i2x2 + -1i2x3 + -35i3 + 35i3 + -7i3x + 7i3x + 5i4 + 1i4x + 245x2 + 49x3) = 0 Combine like terms: -35ix2 + 35ix2 = 0 (0 + -7ix3 + 7ix3 + -245i2 + -49i2x + -5i2x2 + -1i2x3 + -35i3 + 35i3 + -7i3x + 7i3x + 5i4 + 1i4x + 245x2 + 49x3) = 0 (-7ix3 + 7ix3 + -245i2 + -49i2x + -5i2x2 + -1i2x3 + -35i3 + 35i3 + -7i3x + 7i3x + 5i4 + 1i4x + 245x2 + 49x3) = 0 Combine like terms: -7ix3 + 7ix3 = 0 (0 + -245i2 + -49i2x + -5i2x2 + -1i2x3 + -35i3 + 35i3 + -7i3x + 7i3x + 5i4 + 1i4x + 245x2 + 49x3) = 0 (-245i2 + -49i2x + -5i2x2 + -1i2x3 + -35i3 + 35i3 + -7i3x + 7i3x + 5i4 + 1i4x + 245x2 + 49x3) = 0 Combine like terms: -35i3 + 35i3 = 0 (-245i2 + -49i2x + -5i2x2 + -1i2x3 + 0 + -7i3x + 7i3x + 5i4 + 1i4x + 245x2 + 49x3) = 0 (-245i2 + -49i2x + -5i2x2 + -1i2x3 + -7i3x + 7i3x + 5i4 + 1i4x + 245x2 + 49x3) = 0 Combine like terms: -7i3x + 7i3x = 0 (-245i2 + -49i2x + -5i2x2 + -1i2x3 + 0 + 5i4 + 1i4x + 245x2 + 49x3) = 0 (-245i2 + -49i2x + -5i2x2 + -1i2x3 + 5i4 + 1i4x + 245x2 + 49x3) = 0 Solving -245i2 + -49i2x + -5i2x2 + -1i2x3 + 5i4 + 1i4x + 245x2 + 49x3 = 0 Solving for variable 'i'. The solution to this equation could not be determined.
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