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Simplifying (x + 2)(x + -7 + 5i)(x + -7 + -5i) = 0 Reorder the terms: (2 + x)(x + -7 + 5i)(x + -7 + -5i) = 0 Reorder the terms: (2 + x)(-7 + 5i + x)(x + -7 + -5i) = 0 Reorder the terms: (2 + x)(-7 + 5i + x)(-7 + -5i + x) = 0 Multiply (2 + x) * (-7 + 5i + x) (2(-7 + 5i + x) + x(-7 + 5i + x))(-7 + -5i + x) = 0 ((-7 * 2 + 5i * 2 + x * 2) + x(-7 + 5i + x))(-7 + -5i + x) = 0 ((-14 + 10i + 2x) + x(-7 + 5i + x))(-7 + -5i + x) = 0 (-14 + 10i + 2x + (-7 * x + 5i * x + x * x))(-7 + -5i + x) = 0 Reorder the terms: (-14 + 10i + 2x + (5ix + -7x + x2))(-7 + -5i + x) = 0 (-14 + 10i + 2x + (5ix + -7x + x2))(-7 + -5i + x) = 0 Reorder the terms: (-14 + 10i + 5ix + 2x + -7x + x2)(-7 + -5i + x) = 0 Combine like terms: 2x + -7x = -5x (-14 + 10i + 5ix + -5x + x2)(-7 + -5i + x) = 0 Multiply (-14 + 10i + 5ix + -5x + x2) * (-7 + -5i + x) (-14(-7 + -5i + x) + 10i * (-7 + -5i + x) + 5ix * (-7 + -5i + x) + -5x * (-7 + -5i + x) + x2(-7 + -5i + x)) = 0 ((-7 * -14 + -5i * -14 + x * -14) + 10i * (-7 + -5i + x) + 5ix * (-7 + -5i + x) + -5x * (-7 + -5i + x) + x2(-7 + -5i + x)) = 0 ((98 + 70i + -14x) + 10i * (-7 + -5i + x) + 5ix * (-7 + -5i + x) + -5x * (-7 + -5i + x) + x2(-7 + -5i + x)) = 0 (98 + 70i + -14x + (-7 * 10i + -5i * 10i + x * 10i) + 5ix * (-7 + -5i + x) + -5x * (-7 + -5i + x) + x2(-7 + -5i + x)) = 0 Reorder the terms: (98 + 70i + -14x + (-70i + 10ix + -50i2) + 5ix * (-7 + -5i + x) + -5x * (-7 + -5i + x) + x2(-7 + -5i + x)) = 0 (98 + 70i + -14x + (-70i + 10ix + -50i2) + 5ix * (-7 + -5i + x) + -5x * (-7 + -5i + x) + x2(-7 + -5i + x)) = 0 (98 + 70i + -14x + -70i + 10ix + -50i2 + (-7 * 5ix + -5i * 5ix + x * 5ix) + -5x * (-7 + -5i + x) + x2(-7 + -5i + x)) = 0 Reorder the terms: (98 + 70i + -14x + -70i + 10ix + -50i2 + (-35ix + 5ix2 + -25i2x) + -5x * (-7 + -5i + x) + x2(-7 + -5i + x)) = 0 (98 + 70i + -14x + -70i + 10ix + -50i2 + (-35ix + 5ix2 + -25i2x) + -5x * (-7 + -5i + x) + x2(-7 + -5i + x)) = 0 (98 + 70i + -14x + -70i + 10ix + -50i2 + -35ix + 5ix2 + -25i2x + (-7 * -5x + -5i * -5x + x * -5x) + x2(-7 + -5i + x)) = 0 Reorder the terms: (98 + 70i + -14x + -70i + 10ix + -50i2 + -35ix + 5ix2 + -25i2x + (25ix + 35x + -5x2) + x2(-7 + -5i + x)) = 0 (98 + 70i + -14x + -70i + 10ix + -50i2 + -35ix + 5ix2 + -25i2x + (25ix + 35x + -5x2) + x2(-7 + -5i + x)) = 0 (98 + 70i + -14x + -70i + 10ix + -50i2 + -35ix + 5ix2 + -25i2x + 25ix + 35x + -5x2 + (-7 * x2 + -5i * x2 + x * x2)) = 0 Reorder the terms: (98 + 70i + -14x + -70i + 10ix + -50i2 + -35ix + 5ix2 + -25i2x + 25ix + 35x + -5x2 + (-5ix2 + -7x2 + x3)) = 0 (98 + 70i + -14x + -70i + 10ix + -50i2 + -35ix + 5ix2 + -25i2x + 25ix + 35x + -5x2 + (-5ix2 + -7x2 + x3)) = 0 Reorder the terms: (98 + 70i + -70i + 10ix + -35ix + 25ix + 5ix2 + -5ix2 + -50i2 + -25i2x + -14x + 35x + -5x2 + -7x2 + x3) = 0 Combine like terms: 70i + -70i = 0 (98 + 0 + 10ix + -35ix + 25ix + 5ix2 + -5ix2 + -50i2 + -25i2x + -14x + 35x + -5x2 + -7x2 + x3) = 0 (98 + 10ix + -35ix + 25ix + 5ix2 + -5ix2 + -50i2 + -25i2x + -14x + 35x + -5x2 + -7x2 + x3) = 0 Combine like terms: 10ix + -35ix = -25ix (98 + -25ix + 25ix + 5ix2 + -5ix2 + -50i2 + -25i2x + -14x + 35x + -5x2 + -7x2 + x3) = 0 Combine like terms: -25ix + 25ix = 0 (98 + 0 + 5ix2 + -5ix2 + -50i2 + -25i2x + -14x + 35x + -5x2 + -7x2 + x3) = 0 (98 + 5ix2 + -5ix2 + -50i2 + -25i2x + -14x + 35x + -5x2 + -7x2 + x3) = 0 Combine like terms: 5ix2 + -5ix2 = 0 (98 + 0 + -50i2 + -25i2x + -14x + 35x + -5x2 + -7x2 + x3) = 0 (98 + -50i2 + -25i2x + -14x + 35x + -5x2 + -7x2 + x3) = 0 Combine like terms: -14x + 35x = 21x (98 + -50i2 + -25i2x + 21x + -5x2 + -7x2 + x3) = 0 Combine like terms: -5x2 + -7x2 = -12x2 (98 + -50i2 + -25i2x + 21x + -12x2 + x3) = 0 Solving 98 + -50i2 + -25i2x + 21x + -12x2 + x3 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-98' to each side of the equation. 98 + -50i2 + -25i2x + 21x + -12x2 + -98 + x3 = 0 + -98 Reorder the terms: 98 + -98 + -50i2 + -25i2x + 21x + -12x2 + x3 = 0 + -98 Combine like terms: 98 + -98 = 0 0 + -50i2 + -25i2x + 21x + -12x2 + x3 = 0 + -98 -50i2 + -25i2x + 21x + -12x2 + x3 = 0 + -98 Combine like terms: 0 + -98 = -98 -50i2 + -25i2x + 21x + -12x2 + x3 = -98 Add '-21x' to each side of the equation. -50i2 + -25i2x + 21x + -12x2 + -21x + x3 = -98 + -21x Reorder the terms: -50i2 + -25i2x + 21x + -21x + -12x2 + x3 = -98 + -21x Combine like terms: 21x + -21x = 0 -50i2 + -25i2x + 0 + -12x2 + x3 = -98 + -21x -50i2 + -25i2x + -12x2 + x3 = -98 + -21x Add '12x2' to each side of the equation. -50i2 + -25i2x + -12x2 + 12x2 + x3 = -98 + -21x + 12x2 Combine like terms: -12x2 + 12x2 = 0 -50i2 + -25i2x + 0 + x3 = -98 + -21x + 12x2 -50i2 + -25i2x + x3 = -98 + -21x + 12x2 Add '-1x3' to each side of the equation. -50i2 + -25i2x + x3 + -1x3 = -98 + -21x + 12x2 + -1x3 Combine like terms: x3 + -1x3 = 0 -50i2 + -25i2x + 0 = -98 + -21x + 12x2 + -1x3 -50i2 + -25i2x = -98 + -21x + 12x2 + -1x3 Reorder the terms: 98 + -50i2 + -25i2x + 21x + -12x2 + x3 = -98 + -21x + 12x2 + -1x3 + 98 + 21x + -12x2 + x3 Reorder the terms: 98 + -50i2 + -25i2x + 21x + -12x2 + x3 = -98 + 98 + -21x + 21x + 12x2 + -12x2 + -1x3 + x3 Combine like terms: -98 + 98 = 0 98 + -50i2 + -25i2x + 21x + -12x2 + x3 = 0 + -21x + 21x + 12x2 + -12x2 + -1x3 + x3 98 + -50i2 + -25i2x + 21x + -12x2 + x3 = -21x + 21x + 12x2 + -12x2 + -1x3 + x3 Combine like terms: -21x + 21x = 0 98 + -50i2 + -25i2x + 21x + -12x2 + x3 = 0 + 12x2 + -12x2 + -1x3 + x3 98 + -50i2 + -25i2x + 21x + -12x2 + x3 = 12x2 + -12x2 + -1x3 + x3 Combine like terms: 12x2 + -12x2 = 0 98 + -50i2 + -25i2x + 21x + -12x2 + x3 = 0 + -1x3 + x3 98 + -50i2 + -25i2x + 21x + -12x2 + x3 = -1x3 + x3 Combine like terms: -1x3 + x3 = 0 98 + -50i2 + -25i2x + 21x + -12x2 + x3 = 0 The solution to this equation could not be determined.
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