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Simplifying (X + -5 + 2i)(x + 5 + -2i) = 0 Reorder the terms: (-5 + X + 2i)(x + 5 + -2i) = 0 Reorder the terms: (-5 + X + 2i)(5 + -2i + x) = 0 Multiply (-5 + X + 2i) * (5 + -2i + x) (-5(5 + -2i + x) + X(5 + -2i + x) + 2i * (5 + -2i + x)) = 0 ((5 * -5 + -2i * -5 + x * -5) + X(5 + -2i + x) + 2i * (5 + -2i + x)) = 0 ((-25 + 10i + -5x) + X(5 + -2i + x) + 2i * (5 + -2i + x)) = 0 (-25 + 10i + -5x + (5 * X + -2i * X + x * X) + 2i * (5 + -2i + x)) = 0 (-25 + 10i + -5x + (5X + -2iX + xX) + 2i * (5 + -2i + x)) = 0 (-25 + 10i + -5x + 5X + -2iX + xX + (5 * 2i + -2i * 2i + x * 2i)) = 0 Reorder the terms: (-25 + 10i + -5x + 5X + -2iX + xX + (10i + 2ix + -4i2)) = 0 (-25 + 10i + -5x + 5X + -2iX + xX + (10i + 2ix + -4i2)) = 0 Reorder the terms: (-25 + 5X + 10i + 10i + -2iX + 2ix + -4i2 + -5x + xX) = 0 Combine like terms: 10i + 10i = 20i (-25 + 5X + 20i + -2iX + 2ix + -4i2 + -5x + xX) = 0 Solving -25 + 5X + 20i + -2iX + 2ix + -4i2 + -5x + xX = 0 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 5X + 20i + -2iX + 2ix + -4i2 + -5x + 25 + xX = 0 + 25 Reorder the terms: -25 + 25 + 5X + 20i + -2iX + 2ix + -4i2 + -5x + xX = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 5X + 20i + -2iX + 2ix + -4i2 + -5x + xX = 0 + 25 5X + 20i + -2iX + 2ix + -4i2 + -5x + xX = 0 + 25 Combine like terms: 0 + 25 = 25 5X + 20i + -2iX + 2ix + -4i2 + -5x + xX = 25 Add '-20i' to each side of the equation. 5X + 20i + -2iX + 2ix + -4i2 + -5x + -20i + xX = 25 + -20i Reorder the terms: 5X + 20i + -20i + -2iX + 2ix + -4i2 + -5x + xX = 25 + -20i Combine like terms: 20i + -20i = 0 5X + 0 + -2iX + 2ix + -4i2 + -5x + xX = 25 + -20i 5X + -2iX + 2ix + -4i2 + -5x + xX = 25 + -20i Add '-2ix' to each side of the equation. 5X + -2iX + 2ix + -4i2 + -5x + -2ix + xX = 25 + -20i + -2ix Reorder the terms: 5X + -2iX + 2ix + -2ix + -4i2 + -5x + xX = 25 + -20i + -2ix Combine like terms: 2ix + -2ix = 0 5X + -2iX + 0 + -4i2 + -5x + xX = 25 + -20i + -2ix 5X + -2iX + -4i2 + -5x + xX = 25 + -20i + -2ix Add '4i2' to each side of the equation. 5X + -2iX + -4i2 + -5x + 4i2 + xX = 25 + -20i + -2ix + 4i2 Reorder the terms: 5X + -2iX + -4i2 + 4i2 + -5x + xX = 25 + -20i + -2ix + 4i2 Combine like terms: -4i2 + 4i2 = 0 5X + -2iX + 0 + -5x + xX = 25 + -20i + -2ix + 4i2 5X + -2iX + -5x + xX = 25 + -20i + -2ix + 4i2 Add '5x' to each side of the equation. 5X + -2iX + -5x + 5x + xX = 25 + -20i + -2ix + 4i2 + 5x Combine like terms: -5x + 5x = 0 5X + -2iX + 0 + xX = 25 + -20i + -2ix + 4i2 + 5x 5X + -2iX + xX = 25 + -20i + -2ix + 4i2 + 5x Reorder the terms: -25 + 5X + 20i + -2iX + 2ix + -4i2 + -5x + xX = 25 + -20i + -2ix + 4i2 + 5x + -25 + 20i + 2ix + -4i2 + -5x Reorder the terms: -25 + 5X + 20i + -2iX + 2ix + -4i2 + -5x + xX = 25 + -25 + -20i + 20i + -2ix + 2ix + 4i2 + -4i2 + 5x + -5x Combine like terms: 25 + -25 = 0 -25 + 5X + 20i + -2iX + 2ix + -4i2 + -5x + xX = 0 + -20i + 20i + -2ix + 2ix + 4i2 + -4i2 + 5x + -5x -25 + 5X + 20i + -2iX + 2ix + -4i2 + -5x + xX = -20i + 20i + -2ix + 2ix + 4i2 + -4i2 + 5x + -5x Combine like terms: -20i + 20i = 0 -25 + 5X + 20i + -2iX + 2ix + -4i2 + -5x + xX = 0 + -2ix + 2ix + 4i2 + -4i2 + 5x + -5x -25 + 5X + 20i + -2iX + 2ix + -4i2 + -5x + xX = -2ix + 2ix + 4i2 + -4i2 + 5x + -5x Combine like terms: -2ix + 2ix = 0 -25 + 5X + 20i + -2iX + 2ix + -4i2 + -5x + xX = 0 + 4i2 + -4i2 + 5x + -5x -25 + 5X + 20i + -2iX + 2ix + -4i2 + -5x + xX = 4i2 + -4i2 + 5x + -5x Combine like terms: 4i2 + -4i2 = 0 -25 + 5X + 20i + -2iX + 2ix + -4i2 + -5x + xX = 0 + 5x + -5x -25 + 5X + 20i + -2iX + 2ix + -4i2 + -5x + xX = 5x + -5x Combine like terms: 5x + -5x = 0 -25 + 5X + 20i + -2iX + 2ix + -4i2 + -5x + xX = 0 The solution to this equation could not be determined.
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