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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
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
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)
Numerical answer [src] 
y^2 + 5.0*x^2 + x*y
y^2 + 5.0*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)
Trigonometric part [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
Powers [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
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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