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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
Trigonometric part [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
Rational denominator [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
Powers [src] 
   2      2      
- y  - 5*x  + x*y
$$- 5 x^{2} + x y - y^{2}$$ 
-y^2 - 5*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
Combining rational expressions [src] 
     2            
- 5*x  + y*(x - y)
$$- 5 x^{2} + y \left(x - y\right)$$ 
-5*x^2 + y*(x - y)
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