(x-1)(x-1)(x-(5-2i))(x-(5+2i))=0

Simple and best practice solution for (x-1)(x-1)(x-(5-2i))(x-(5+2i))=0 equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

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Solution for (x-1)(x-1)(x-(5-2i))(x-(5+2i))=0 equation:

Simplifying
(x + -1)(x + -1)(x + -1(5 + -2i))(x + -1(5 + 2i)) = 0

Reorder the terms:
(-1 + x)(x + -1)(x + -1(5 + -2i))(x + -1(5 + 2i)) = 0

Reorder the terms:
(-1 + x)(-1 + x)(x + -1(5 + -2i))(x + -1(5 + 2i)) = 0
(-1 + x)(-1 + x)(x + (5 * -1 + -2i * -1))(x + -1(5 + 2i)) = 0
(-1 + x)(-1 + x)(x + (-5 + 2i))(x + -1(5 + 2i)) = 0

Reorder the terms:
(-1 + x)(-1 + x)(-5 + 2i + x)(x + -1(5 + 2i)) = 0
(-1 + x)(-1 + x)(-5 + 2i + x)(x + (5 * -1 + 2i * -1)) = 0
(-1 + x)(-1 + x)(-5 + 2i + x)(x + (-5 + -2i)) = 0

Reorder the terms:
(-1 + x)(-1 + x)(-5 + 2i + x)(-5 + -2i + x) = 0

Multiply (-1 + x) * (-1 + x)
(-1(-1 + x) + x(-1 + x))(-5 + 2i + x)(-5 + -2i + x) = 0
((-1 * -1 + x * -1) + x(-1 + x))(-5 + 2i + x)(-5 + -2i + x) = 0
((1 + -1x) + x(-1 + x))(-5 + 2i + x)(-5 + -2i + x) = 0
(1 + -1x + (-1 * x + x * x))(-5 + 2i + x)(-5 + -2i + x) = 0
(1 + -1x + (-1x + x²))(-5 + 2i + x)(-5 + -2i + x) = 0

Combine like terms: -1x + -1x = -2x
(1 + -2x + x²)(-5 + 2i + x)(-5 + -2i + x) = 0

Multiply (1 + -2x + x²) * (-5 + 2i + x)
(1(-5 + 2i + x) + -2x * (-5 + 2i + x) + x²(-5 + 2i + x))(-5 + -2i + x) = 0
((-5 * 1 + 2i * 1 + x * 1) + -2x * (-5 + 2i + x) + x²(-5 + 2i + x))(-5 + -2i + x) = 0
((-5 + 2i + 1x) + -2x * (-5 + 2i + x) + x²(-5 + 2i + x))(-5 + -2i + x) = 0
(-5 + 2i + 1x + (-5 * -2x + 2i * -2x + x * -2x) + x²(-5 + 2i + x))(-5 + -2i + x) = 0

Reorder the terms:
(-5 + 2i + 1x + (-4ix + 10x + -2x²) + x²(-5 + 2i + x))(-5 + -2i + x) = 0
(-5 + 2i + 1x + (-4ix + 10x + -2x²) + x²(-5 + 2i + x))(-5 + -2i + x) = 0
(-5 + 2i + 1x + -4ix + 10x + -2x² + (-5 * x² + 2i * x² + x * x²))(-5 + -2i + x) = 0

Reorder the terms:
(-5 + 2i + 1x + -4ix + 10x + -2x² + (2ix² + -5x² + x³))(-5 + -2i + x) = 0
(-5 + 2i + 1x + -4ix + 10x + -2x² + (2ix² + -5x² + x³))(-5 + -2i + x) = 0

Reorder the terms:
(-5 + 2i + -4ix + 2ix² + 1x + 10x + -2x² + -5x² + x³)(-5 + -2i + x) = 0

Combine like terms: 1x + 10x = 11x
(-5 + 2i + -4ix + 2ix² + 11x + -2x² + -5x² + x³)(-5 + -2i + x) = 0

Combine like terms: -2x² + -5x² = -7x²
(-5 + 2i + -4ix + 2ix² + 11x + -7x² + x³)(-5 + -2i + x) = 0

Multiply (-5 + 2i + -4ix + 2ix² + 11x + -7x² + x³) * (-5 + -2i + x)
(-5(-5 + -2i + x) + 2i * (-5 + -2i + x) + -4ix * (-5 + -2i + x) + 2ix² * (-5 + -2i + x) + 11x * (-5 + -2i + x) + -7x² * (-5 + -2i + x) + x³(-5 + -2i + x)) = 0
((-5 * -5 + -2i * -5 + x * -5) + 2i * (-5 + -2i + x) + -4ix * (-5 + -2i + x) + 2ix² * (-5 + -2i + x) + 11x * (-5 + -2i + x) + -7x² * (-5 + -2i + x) + x³(-5 + -2i + x)) = 0
((25 + 10i + -5x) + 2i * (-5 + -2i + x) + -4ix * (-5 + -2i + x) + 2ix² * (-5 + -2i + x) + 11x * (-5 + -2i + x) + -7x² * (-5 + -2i + x) + x³(-5 + -2i + x)) = 0
(25 + 10i + -5x + (-5 * 2i + -2i * 2i + x * 2i) + -4ix * (-5 + -2i + x) + 2ix² * (-5 + -2i + x) + 11x * (-5 + -2i + x) + -7x² * (-5 + -2i + x) + x³(-5 + -2i + x)) = 0

Reorder the terms:
(25 + 10i + -5x + (-10i + 2ix + -4i²) + -4ix * (-5 + -2i + x) + 2ix² * (-5 + -2i + x) + 11x * (-5 + -2i + x) + -7x² * (-5 + -2i + x) + x³(-5 + -2i + x)) = 0
(25 + 10i + -5x + (-10i + 2ix + -4i²) + -4ix * (-5 + -2i + x) + 2ix² * (-5 + -2i + x) + 11x * (-5 + -2i + x) + -7x² * (-5 + -2i + x) + x³(-5 + -2i + x)) = 0
(25 + 10i + -5x + -10i + 2ix + -4i² + (-5 * -4ix + -2i * -4ix + x * -4ix) + 2ix² * (-5 + -2i + x) + 11x * (-5 + -2i + x) + -7x² * (-5 + -2i + x) + x³(-5 + -2i + x)) = 0

Reorder the terms:
(25 + 10i + -5x + -10i + 2ix + -4i² + (20ix + -4ix² + 8i²x) + 2ix² * (-5 + -2i + x) + 11x * (-5 + -2i + x) + -7x² * (-5 + -2i + x) + x³(-5 + -2i + x)) = 0
(25 + 10i + -5x + -10i + 2ix + -4i² + (20ix + -4ix² + 8i²x) + 2ix² * (-5 + -2i + x) + 11x * (-5 + -2i + x) + -7x² * (-5 + -2i + x) + x³(-5 + -2i + x)) = 0
(25 + 10i + -5x + -10i + 2ix + -4i² + 20ix + -4ix² + 8i²x + (-5 * 2ix² + -2i * 2ix² + x * 2ix²) + 11x * (-5 + -2i + x) + -7x² * (-5 + -2i + x) + x³(-5 + -2i + x)) = 0

Reorder the terms:
(25 + 10i + -5x + -10i + 2ix + -4i² + 20ix + -4ix² + 8i²x + (-10ix² + 2ix³ + -4i²x²) + 11x * (-5 + -2i + x) + -7x² * (-5 + -2i + x) + x³(-5 + -2i + x)) = 0
(25 + 10i + -5x + -10i + 2ix + -4i² + 20ix + -4ix² + 8i²x + (-10ix² + 2ix³ + -4i²x²) + 11x * (-5 + -2i + x) + -7x² * (-5 + -2i + x) + x³(-5 + -2i + x)) = 0
(25 + 10i + -5x + -10i + 2ix + -4i² + 20ix + -4ix² + 8i²x + -10ix² + 2ix³ + -4i²x² + (-5 * 11x + -2i * 11x + x * 11x) + -7x² * (-5 + -2i + x) + x³(-5 + -2i + x)) = 0

Reorder the terms:
(25 + 10i + -5x + -10i + 2ix + -4i² + 20ix + -4ix² + 8i²x + -10ix² + 2ix³ + -4i²x² + (-22ix + -55x + 11x²) + -7x² * (-5 + -2i + x) + x³(-5 + -2i + x)) = 0
(25 + 10i + -5x + -10i + 2ix + -4i² + 20ix + -4ix² + 8i²x + -10ix² + 2ix³ + -4i²x² + (-22ix + -55x + 11x²) + -7x² * (-5 + -2i + x) + x³(-5 + -2i + x)) = 0
(25 + 10i + -5x + -10i + 2ix + -4i² + 20ix + -4ix² + 8i²x + -10ix² + 2ix³ + -4i²x² + -22ix + -55x + 11x² + (-5 * -7x² + -2i * -7x² + x * -7x²) + x³(-5 + -2i + x)) = 0

Reorder the terms:
(25 + 10i + -5x + -10i + 2ix + -4i² + 20ix + -4ix² + 8i²x + -10ix² + 2ix³ + -4i²x² + -22ix + -55x + 11x² + (14ix² + 35x² + -7x³) + x³(-5 + -2i + x)) = 0
(25 + 10i + -5x + -10i + 2ix + -4i² + 20ix + -4ix² + 8i²x + -10ix² + 2ix³ + -4i²x² + -22ix + -55x + 11x² + (14ix² + 35x² + -7x³) + x³(-5 + -2i + x)) = 0
(25 + 10i + -5x + -10i + 2ix + -4i² + 20ix + -4ix² + 8i²x + -10ix² + 2ix³ + -4i²x² + -22ix + -55x + 11x² + 14ix² + 35x² + -7x³ + (-5 * x³ + -2i * x³ + x * x³)) = 0

Reorder the terms:
(25 + 10i + -5x + -10i + 2ix + -4i² + 20ix + -4ix² + 8i²x + -10ix² + 2ix³ + -4i²x² + -22ix + -55x + 11x² + 14ix² + 35x² + -7x³ + (-2ix³ + -5x³ + x⁴)) = 0
(25 + 10i + -5x + -10i + 2ix + -4i² + 20ix + -4ix² + 8i²x + -10ix² + 2ix³ + -4i²x² + -22ix + -55x + 11x² + 14ix² + 35x² + -7x³ + (-2ix³ + -5x³ + x⁴)) = 0

Reorder the terms:
(25 + 10i + -10i + 2ix + 20ix + -22ix + -4ix² + -10ix² + 14ix² + 2ix³ + -2ix³ + -4i² + 8i²x + -4i²x² + -5x + -55x + 11x² + 35x² + -7x³ + -5x³ + x⁴) = 0

Combine like terms: 10i + -10i = 0
(25 + 0 + 2ix + 20ix + -22ix + -4ix² + -10ix² + 14ix² + 2ix³ + -2ix³ + -4i² + 8i²x + -4i²x² + -5x + -55x + 11x² + 35x² + -7x³ + -5x³ + x⁴) = 0
(25 + 2ix + 20ix + -22ix + -4ix² + -10ix² + 14ix² + 2ix³ + -2ix³ + -4i² + 8i²x + -4i²x² + -5x + -55x + 11x² + 35x² + -7x³ + -5x³ + x⁴) = 0

Combine like terms: 2ix + 20ix = 22ix
(25 + 22ix + -22ix + -4ix² + -10ix² + 14ix² + 2ix³ + -2ix³ + -4i² + 8i²x + -4i²x² + -5x + -55x + 11x² + 35x² + -7x³ + -5x³ + x⁴) = 0

Combine like terms: 22ix + -22ix = 0
(25 + 0 + -4ix² + -10ix² + 14ix² + 2ix³ + -2ix³ + -4i² + 8i²x + -4i²x² + -5x + -55x + 11x² + 35x² + -7x³ + -5x³ + x⁴) = 0
(25 + -4ix² + -10ix² + 14ix² + 2ix³ + -2ix³ + -4i² + 8i²x + -4i²x² + -5x + -55x + 11x² + 35x² + -7x³ + -5x³ + x⁴) = 0

Combine like terms: -4ix² + -10ix² = -14ix²
(25 + -14ix² + 14ix² + 2ix³ + -2ix³ + -4i² + 8i²x + -4i²x² + -5x + -55x + 11x² + 35x² + -7x³ + -5x³ + x⁴) = 0

Combine like terms: -14ix² + 14ix² = 0
(25 + 0 + 2ix³ + -2ix³ + -4i² + 8i²x + -4i²x² + -5x + -55x + 11x² + 35x² + -7x³ + -5x³ + x⁴) = 0
(25 + 2ix³ + -2ix³ + -4i² + 8i²x + -4i²x² + -5x + -55x + 11x² + 35x² + -7x³ + -5x³ + x⁴) = 0

Combine like terms: 2ix³ + -2ix³ = 0
(25 + 0 + -4i² + 8i²x + -4i²x² + -5x + -55x + 11x² + 35x² + -7x³ + -5x³ + x⁴) = 0
(25 + -4i² + 8i²x + -4i²x² + -5x + -55x + 11x² + 35x² + -7x³ + -5x³ + x⁴) = 0

Combine like terms: -5x + -55x = -60x
(25 + -4i² + 8i²x + -4i²x² + -60x + 11x² + 35x² + -7x³ + -5x³ + x⁴) = 0

Combine like terms: 11x² + 35x² = 46x²
(25 + -4i² + 8i²x + -4i²x² + -60x + 46x² + -7x³ + -5x³ + x⁴) = 0

Combine like terms: -7x³ + -5x³ = -12x³
(25 + -4i² + 8i²x + -4i²x² + -60x + 46x² + -12x³ + x⁴) = 0

Solving
25 + -4i² + 8i²x + -4i²x² + -60x + 46x² + -12x³ + x⁴ = 0

Solving for variable 'i'.

Move all terms containing i to the left, all other terms to the right.

Add '-25' to each side of the equation.
25 + -4i² + 8i²x + -4i²x² + -60x + 46x² + -12x³ + -25 + x⁴ = 0 + -25

Reorder the terms:
25 + -25 + -4i² + 8i²x + -4i²x² + -60x + 46x² + -12x³ + x⁴ = 0 + -25

Combine like terms: 25 + -25 = 0
0 + -4i² + 8i²x + -4i²x² + -60x + 46x² + -12x³ + x⁴ = 0 + -25
-4i² + 8i²x + -4i²x² + -60x + 46x² + -12x³ + x⁴ = 0 + -25

Combine like terms: 0 + -25 = -25
-4i² + 8i²x + -4i²x² + -60x + 46x² + -12x³ + x⁴ = -25

Add '60x' to each side of the equation.
-4i² + 8i²x + -4i²x² + -60x + 46x² + -12x³ + 60x + x⁴ = -25 + 60x

Reorder the terms:
-4i² + 8i²x + -4i²x² + -60x + 60x + 46x² + -12x³ + x⁴ = -25 + 60x

Combine like terms: -60x + 60x = 0
-4i² + 8i²x + -4i²x² + 0 + 46x² + -12x³ + x⁴ = -25 + 60x
-4i² + 8i²x + -4i²x² + 46x² + -12x³ + x⁴ = -25 + 60x

Add '-46x²' to each side of the equation.
-4i² + 8i²x + -4i²x² + 46x² + -12x³ + -46x² + x⁴ = -25 + 60x + -46x²

Reorder the terms:
-4i² + 8i²x + -4i²x² + 46x² + -46x² + -12x³ + x⁴ = -25 + 60x + -46x²

Combine like terms: 46x² + -46x² = 0
-4i² + 8i²x + -4i²x² + 0 + -12x³ + x⁴ = -25 + 60x + -46x²
-4i² + 8i²x + -4i²x² + -12x³ + x⁴ = -25 + 60x + -46x²

Add '12x³' to each side of the equation.
-4i² + 8i²x + -4i²x² + -12x³ + 12x³ + x⁴ = -25 + 60x + -46x² + 12x³

Combine like terms: -12x³ + 12x³ = 0
-4i² + 8i²x + -4i²x² + 0 + x⁴ = -25 + 60x + -46x² + 12x³
-4i² + 8i²x + -4i²x² + x⁴ = -25 + 60x + -46x² + 12x³

Add '-1x⁴' to each side of the equation.
-4i² + 8i²x + -4i²x² + x⁴ + -1x⁴ = -25 + 60x + -46x² + 12x³ + -1x⁴

Combine like terms: x⁴ + -1x⁴ = 0
-4i² + 8i²x + -4i²x² + 0 = -25 + 60x + -46x² + 12x³ + -1x⁴
-4i² + 8i²x + -4i²x² = -25 + 60x + -46x² + 12x³ + -1x⁴

Reorder the terms:
25 + -4i² + 8i²x + -4i²x² + -60x + 46x² + -12x³ + x⁴ = -25 + 60x + -46x² + 12x³ + -1x⁴ + 25 + -60x + 46x² + -12x³ + x⁴

Reorder the terms:
25 + -4i² + 8i²x + -4i²x² + -60x + 46x² + -12x³ + x⁴ = -25 + 25 + 60x + -60x + -46x² + 46x² + 12x³ + -12x³ + -1x⁴ + x⁴

Combine like terms: -25 + 25 = 0
25 + -4i² + 8i²x + -4i²x² + -60x + 46x² + -12x³ + x⁴ = 0 + 60x + -60x + -46x² + 46x² + 12x³ + -12x³ + -1x⁴ + x⁴
25 + -4i² + 8i²x + -4i²x² + -60x + 46x² + -12x³ + x⁴ = 60x + -60x + -46x² + 46x² + 12x³ + -12x³ + -1x⁴ + x⁴

Combine like terms: 60x + -60x = 0
25 + -4i² + 8i²x + -4i²x² + -60x + 46x² + -12x³ + x⁴ = 0 + -46x² + 46x² + 12x³ + -12x³ + -1x⁴ + x⁴
25 + -4i² + 8i²x + -4i²x² + -60x + 46x² + -12x³ + x⁴ = -46x² + 46x² + 12x³ + -12x³ + -1x⁴ + x⁴

Combine like terms: -46x² + 46x² = 0
25 + -4i² + 8i²x + -4i²x² + -60x + 46x² + -12x³ + x⁴ = 0 + 12x³ + -12x³ + -1x⁴ + x⁴
25 + -4i² + 8i²x + -4i²x² + -60x + 46x² + -12x³ + x⁴ = 12x³ + -12x³ + -1x⁴ + x⁴

Combine like terms: 12x³ + -12x³ = 0
25 + -4i² + 8i²x + -4i²x² + -60x + 46x² + -12x³ + x⁴ = 0 + -1x⁴ + x⁴
25 + -4i² + 8i²x + -4i²x² + -60x + 46x² + -12x³ + x⁴ = -1x⁴ + x⁴

Combine like terms: -1x⁴ + x⁴ = 0
25 + -4i² + 8i²x + -4i²x² + -60x + 46x² + -12x³ + x⁴ = 0

The solution to this equation could not be determined.

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(x-1)(x-1)(x-(5-2i))(x-(5+2i))=0

Simple and best practice solution for (x-1)(x-1)(x-(5-2i))(x-(5+2i))=0 equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

Solution for (x-1)(x-1)(x-(5-2i))(x-(5+2i))=0 equation:

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