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Expression simplification/ Factor perfect squares/ y^2-y*x+5*x^2

Factor y^2-y*x+5*x^2 squared

An expression to simplify:

The solution

You have entered [src] 
 2            2
y  - y*x + 5*x
$$5 x^{2} + \left(- x y + y^{2}\right)$$ 
y^2 - y*x + 5*x^2
Factorization [src] 
/      /        ____\\ /      /        ____\\
|    y*\1 - I*\/ 19 /| |    y*\1 + I*\/ 19 /|
|x - ----------------|*|x - ----------------|
\           10       / \           10       /
$$\left(x - \frac{y \left(1 - \sqrt{19} i\right)}{10}\right) \left(x - \frac{y \left(1 + \sqrt{19} i\right)}{10}\right)$$ 
(x - y*(1 - i*sqrt(19))/10)*(x - y*(1 + i*sqrt(19))/10)
The perfect square
Let's highlight the perfect square of the square three-member
$$5 x^{2} + \left(- x y + y^{2}\right)$$
Let us write down the identical expression
$$5 x^{2} + \left(- x y + y^{2}\right) = \frac{19 y^{2}}{20} + \left(5 x^{2} - x y + \frac{y^{2}}{20}\right)$$
or
$$5 x^{2} + \left(- x y + y^{2}\right) = \frac{19 y^{2}}{20} + \left(\sqrt{5} x - \frac{\sqrt{5} y}{10}\right)^{2}$$
General simplification [src] 
 2      2      
y  + 5*x  - x*y
$$5 x^{2} - x y + y^{2}$$ 
y^2 + 5*x^2 - x*y
Numerical answer [src] 
y^2 + 5.0*x^2 - x*y
y^2 + 5.0*x^2 - x*y
Combinatorics [src] 
 2      2      
y  + 5*x  - x*y
$$5 x^{2} - x y + y^{2}$$ 
y^2 + 5*x^2 - x*y
Assemble expression [src] 
 2      2      
y  + 5*x  - x*y
$$5 x^{2} - x y + y^{2}$$ 
y^2 + 5*x^2 - x*y
Trigonometric part [src] 
 2      2      
y  + 5*x  - x*y
$$5 x^{2} - x y + y^{2}$$ 
y^2 + 5*x^2 - x*y
Powers [src] 
 2      2      
y  + 5*x  - x*y
$$5 x^{2} - x y + y^{2}$$ 
y^2 + 5*x^2 - x*y
Combining rational expressions [src] 
   2            
5*x  + y*(y - x)
$$5 x^{2} + y \left(- x + y\right)$$ 
5*x^2 + y*(y - x)
Rational denominator [src] 
 2      2      
y  + 5*x  - x*y
$$5 x^{2} - x y + y^{2}$$ 
y^2 + 5*x^2 - x*y
Common denominator [src] 
 2      2      
y  + 5*x  - x*y
$$5 x^{2} - x y + y^{2}$$ 
y^2 + 5*x^2 - x*y
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