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Simplifying (x + -5)(x + -1 + -2i)(x + -1 + 2i) = 0 Reorder the terms: (-5 + x)(x + -1 + -2i)(x + -1 + 2i) = 0 Reorder the terms: (-5 + x)(-1 + -2i + x)(x + -1 + 2i) = 0 Reorder the terms: (-5 + x)(-1 + -2i + x)(-1 + 2i + x) = 0 Multiply (-5 + x) * (-1 + -2i + x) (-5(-1 + -2i + x) + x(-1 + -2i + x))(-1 + 2i + x) = 0 ((-1 * -5 + -2i * -5 + x * -5) + x(-1 + -2i + x))(-1 + 2i + x) = 0 ((5 + 10i + -5x) + x(-1 + -2i + x))(-1 + 2i + x) = 0 (5 + 10i + -5x + (-1 * x + -2i * x + x * x))(-1 + 2i + x) = 0 Reorder the terms: (5 + 10i + -5x + (-2ix + -1x + x2))(-1 + 2i + x) = 0 (5 + 10i + -5x + (-2ix + -1x + x2))(-1 + 2i + x) = 0 Reorder the terms: (5 + 10i + -2ix + -5x + -1x + x2)(-1 + 2i + x) = 0 Combine like terms: -5x + -1x = -6x (5 + 10i + -2ix + -6x + x2)(-1 + 2i + x) = 0 Multiply (5 + 10i + -2ix + -6x + x2) * (-1 + 2i + x) (5(-1 + 2i + x) + 10i * (-1 + 2i + x) + -2ix * (-1 + 2i + x) + -6x * (-1 + 2i + x) + x2(-1 + 2i + x)) = 0 ((-1 * 5 + 2i * 5 + x * 5) + 10i * (-1 + 2i + x) + -2ix * (-1 + 2i + x) + -6x * (-1 + 2i + x) + x2(-1 + 2i + x)) = 0 ((-5 + 10i + 5x) + 10i * (-1 + 2i + x) + -2ix * (-1 + 2i + x) + -6x * (-1 + 2i + x) + x2(-1 + 2i + x)) = 0 (-5 + 10i + 5x + (-1 * 10i + 2i * 10i + x * 10i) + -2ix * (-1 + 2i + x) + -6x * (-1 + 2i + x) + x2(-1 + 2i + x)) = 0 Reorder the terms: (-5 + 10i + 5x + (-10i + 10ix + 20i2) + -2ix * (-1 + 2i + x) + -6x * (-1 + 2i + x) + x2(-1 + 2i + x)) = 0 (-5 + 10i + 5x + (-10i + 10ix + 20i2) + -2ix * (-1 + 2i + x) + -6x * (-1 + 2i + x) + x2(-1 + 2i + x)) = 0 (-5 + 10i + 5x + -10i + 10ix + 20i2 + (-1 * -2ix + 2i * -2ix + x * -2ix) + -6x * (-1 + 2i + x) + x2(-1 + 2i + x)) = 0 Reorder the terms: (-5 + 10i + 5x + -10i + 10ix + 20i2 + (2ix + -2ix2 + -4i2x) + -6x * (-1 + 2i + x) + x2(-1 + 2i + x)) = 0 (-5 + 10i + 5x + -10i + 10ix + 20i2 + (2ix + -2ix2 + -4i2x) + -6x * (-1 + 2i + x) + x2(-1 + 2i + x)) = 0 (-5 + 10i + 5x + -10i + 10ix + 20i2 + 2ix + -2ix2 + -4i2x + (-1 * -6x + 2i * -6x + x * -6x) + x2(-1 + 2i + x)) = 0 Reorder the terms: (-5 + 10i + 5x + -10i + 10ix + 20i2 + 2ix + -2ix2 + -4i2x + (-12ix + 6x + -6x2) + x2(-1 + 2i + x)) = 0 (-5 + 10i + 5x + -10i + 10ix + 20i2 + 2ix + -2ix2 + -4i2x + (-12ix + 6x + -6x2) + x2(-1 + 2i + x)) = 0 (-5 + 10i + 5x + -10i + 10ix + 20i2 + 2ix + -2ix2 + -4i2x + -12ix + 6x + -6x2 + (-1 * x2 + 2i * x2 + x * x2)) = 0 Reorder the terms: (-5 + 10i + 5x + -10i + 10ix + 20i2 + 2ix + -2ix2 + -4i2x + -12ix + 6x + -6x2 + (2ix2 + -1x2 + x3)) = 0 (-5 + 10i + 5x + -10i + 10ix + 20i2 + 2ix + -2ix2 + -4i2x + -12ix + 6x + -6x2 + (2ix2 + -1x2 + x3)) = 0 Reorder the terms: (-5 + 10i + -10i + 10ix + 2ix + -12ix + -2ix2 + 2ix2 + 20i2 + -4i2x + 5x + 6x + -6x2 + -1x2 + x3) = 0 Combine like terms: 10i + -10i = 0 (-5 + 0 + 10ix + 2ix + -12ix + -2ix2 + 2ix2 + 20i2 + -4i2x + 5x + 6x + -6x2 + -1x2 + x3) = 0 (-5 + 10ix + 2ix + -12ix + -2ix2 + 2ix2 + 20i2 + -4i2x + 5x + 6x + -6x2 + -1x2 + x3) = 0 Combine like terms: 10ix + 2ix = 12ix (-5 + 12ix + -12ix + -2ix2 + 2ix2 + 20i2 + -4i2x + 5x + 6x + -6x2 + -1x2 + x3) = 0 Combine like terms: 12ix + -12ix = 0 (-5 + 0 + -2ix2 + 2ix2 + 20i2 + -4i2x + 5x + 6x + -6x2 + -1x2 + x3) = 0 (-5 + -2ix2 + 2ix2 + 20i2 + -4i2x + 5x + 6x + -6x2 + -1x2 + x3) = 0 Combine like terms: -2ix2 + 2ix2 = 0 (-5 + 0 + 20i2 + -4i2x + 5x + 6x + -6x2 + -1x2 + x3) = 0 (-5 + 20i2 + -4i2x + 5x + 6x + -6x2 + -1x2 + x3) = 0 Combine like terms: 5x + 6x = 11x (-5 + 20i2 + -4i2x + 11x + -6x2 + -1x2 + x3) = 0 Combine like terms: -6x2 + -1x2 = -7x2 (-5 + 20i2 + -4i2x + 11x + -7x2 + x3) = 0 Solving -5 + 20i2 + -4i2x + 11x + -7x2 + x3 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 20i2 + -4i2x + 11x + -7x2 + 5 + x3 = 0 + 5 Reorder the terms: -5 + 5 + 20i2 + -4i2x + 11x + -7x2 + x3 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 20i2 + -4i2x + 11x + -7x2 + x3 = 0 + 5 20i2 + -4i2x + 11x + -7x2 + x3 = 0 + 5 Combine like terms: 0 + 5 = 5 20i2 + -4i2x + 11x + -7x2 + x3 = 5 Add '-11x' to each side of the equation. 20i2 + -4i2x + 11x + -7x2 + -11x + x3 = 5 + -11x Reorder the terms: 20i2 + -4i2x + 11x + -11x + -7x2 + x3 = 5 + -11x Combine like terms: 11x + -11x = 0 20i2 + -4i2x + 0 + -7x2 + x3 = 5 + -11x 20i2 + -4i2x + -7x2 + x3 = 5 + -11x Add '7x2' to each side of the equation. 20i2 + -4i2x + -7x2 + 7x2 + x3 = 5 + -11x + 7x2 Combine like terms: -7x2 + 7x2 = 0 20i2 + -4i2x + 0 + x3 = 5 + -11x + 7x2 20i2 + -4i2x + x3 = 5 + -11x + 7x2 Add '-1x3' to each side of the equation. 20i2 + -4i2x + x3 + -1x3 = 5 + -11x + 7x2 + -1x3 Combine like terms: x3 + -1x3 = 0 20i2 + -4i2x + 0 = 5 + -11x + 7x2 + -1x3 20i2 + -4i2x = 5 + -11x + 7x2 + -1x3 Reorder the terms: -5 + 20i2 + -4i2x + 11x + -7x2 + x3 = 5 + -11x + 7x2 + -1x3 + -5 + 11x + -7x2 + x3 Reorder the terms: -5 + 20i2 + -4i2x + 11x + -7x2 + x3 = 5 + -5 + -11x + 11x + 7x2 + -7x2 + -1x3 + x3 Combine like terms: 5 + -5 = 0 -5 + 20i2 + -4i2x + 11x + -7x2 + x3 = 0 + -11x + 11x + 7x2 + -7x2 + -1x3 + x3 -5 + 20i2 + -4i2x + 11x + -7x2 + x3 = -11x + 11x + 7x2 + -7x2 + -1x3 + x3 Combine like terms: -11x + 11x = 0 -5 + 20i2 + -4i2x + 11x + -7x2 + x3 = 0 + 7x2 + -7x2 + -1x3 + x3 -5 + 20i2 + -4i2x + 11x + -7x2 + x3 = 7x2 + -7x2 + -1x3 + x3 Combine like terms: 7x2 + -7x2 = 0 -5 + 20i2 + -4i2x + 11x + -7x2 + x3 = 0 + -1x3 + x3 -5 + 20i2 + -4i2x + 11x + -7x2 + x3 = -1x3 + x3 Combine like terms: -1x3 + x3 = 0 -5 + 20i2 + -4i2x + 11x + -7x2 + x3 = 0 The solution to this equation could not be determined.
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