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

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


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

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

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

Multiply (-5 + 2i + x) * (-5 + -2i + x)
(-5(-5 + -2i + x) + 2i * (-5 + -2i + x) + x(-5 + -2i + x)) = 0
((-5 * -5 + -2i * -5 + x * -5) + 2i * (-5 + -2i + x) + x(-5 + -2i + x)) = 0
((25 + 10i + -5x) + 2i * (-5 + -2i + x) + x(-5 + -2i + x)) = 0
(25 + 10i + -5x + (-5 * 2i + -2i * 2i + x * 2i) + x(-5 + -2i + x)) = 0

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

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

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

Combine like terms: 10i + -10i = 0
(25 + 0 + 2ix + -2ix + -4i2 + -5x + -5x + x2) = 0
(25 + 2ix + -2ix + -4i2 + -5x + -5x + x2) = 0

Combine like terms: 2ix + -2ix = 0
(25 + 0 + -4i2 + -5x + -5x + x2) = 0
(25 + -4i2 + -5x + -5x + x2) = 0

Combine like terms: -5x + -5x = -10x
(25 + -4i2 + -10x + x2) = 0

Solving
25 + -4i2 + -10x + x2 = 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 + -10x + -25 + x2 = 0 + -25

Reorder the terms:
25 + -25 + -4i2 + -10x + x2 = 0 + -25

Combine like terms: 25 + -25 = 0
0 + -4i2 + -10x + x2 = 0 + -25
-4i2 + -10x + x2 = 0 + -25

Combine like terms: 0 + -25 = -25
-4i2 + -10x + x2 = -25

Add '10x' to each side of the equation.
-4i2 + -10x + 10x + x2 = -25 + 10x

Combine like terms: -10x + 10x = 0
-4i2 + 0 + x2 = -25 + 10x
-4i2 + x2 = -25 + 10x

Add '-1x2' to each side of the equation.
-4i2 + x2 + -1x2 = -25 + 10x + -1x2

Combine like terms: x2 + -1x2 = 0
-4i2 + 0 = -25 + 10x + -1x2
-4i2 = -25 + 10x + -1x2

Divide each side by '-4'.
i2 = 6.25 + -2.5x + 0.25x2

Simplifying
i2 = 6.25 + -2.5x + 0.25x2

Reorder the terms:
-6.25 + i2 + 2.5x + -0.25x2 = 6.25 + -2.5x + 0.25x2 + -6.25 + 2.5x + -0.25x2

Reorder the terms:
-6.25 + i2 + 2.5x + -0.25x2 = 6.25 + -6.25 + -2.5x + 2.5x + 0.25x2 + -0.25x2

Combine like terms: 6.25 + -6.25 = 0.00
-6.25 + i2 + 2.5x + -0.25x2 = 0.00 + -2.5x + 2.5x + 0.25x2 + -0.25x2
-6.25 + i2 + 2.5x + -0.25x2 = -2.5x + 2.5x + 0.25x2 + -0.25x2

Combine like terms: -2.5x + 2.5x = 0.0
-6.25 + i2 + 2.5x + -0.25x2 = 0.0 + 0.25x2 + -0.25x2
-6.25 + i2 + 2.5x + -0.25x2 = 0.25x2 + -0.25x2

Combine like terms: 0.25x2 + -0.25x2 = 0.00
-6.25 + i2 + 2.5x + -0.25x2 = 0.00

The solution to this equation could not be determined.

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