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

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

An expression to simplify:

The solution

You have entered [src] 
   2            2
- y  - 5*y*x + x
$$x^{2} + \left(- x 5 y - y^{2}\right)$$ 
-y^2 - 5*y*x + x^2
The perfect square
Let's highlight the perfect square of the square three-member
$$x^{2} + \left(- x 5 y - y^{2}\right)$$
Let us write down the identical expression
$$x^{2} + \left(- x 5 y - y^{2}\right) = - \frac{29 y^{2}}{4} + \left(x^{2} - 5 x y + \frac{25 y^{2}}{4}\right)$$
or
$$x^{2} + \left(- x 5 y - y^{2}\right) = - \frac{29 y^{2}}{4} + \left(x - \frac{5 y}{2}\right)^{2}$$
in the view of the product
$$\left(- \sqrt{\frac{29}{4}} y + \left(x - \frac{5 y}{2}\right)\right) \left(\sqrt{\frac{29}{4}} y + \left(x - \frac{5 y}{2}\right)\right)$$
$$\left(- \frac{\sqrt{29}}{2} y + \left(x - \frac{5 y}{2}\right)\right) \left(\frac{\sqrt{29}}{2} y + \left(x - \frac{5 y}{2}\right)\right)$$
$$\left(x + y \left(- \frac{5}{2} + \frac{\sqrt{29}}{2}\right)\right) \left(x + y \left(- \frac{\sqrt{29}}{2} - \frac{5}{2}\right)\right)$$
$$\left(x + y \left(- \frac{5}{2} + \frac{\sqrt{29}}{2}\right)\right) \left(x + y \left(- \frac{\sqrt{29}}{2} - \frac{5}{2}\right)\right)$$
General simplification [src] 
 2    2        
x  - y  - 5*x*y
$$x^{2} - 5 x y - y^{2}$$ 
x^2 - y^2 - 5*x*y
Factorization [src] 
/      /      ____\\ /      /      ____\\
|    y*\5 - \/ 29 /| |    y*\5 + \/ 29 /|
|x - --------------|*|x - --------------|
\          2       / \          2       /
$$\left(x - \frac{y \left(5 - \sqrt{29}\right)}{2}\right) \left(x - \frac{y \left(5 + \sqrt{29}\right)}{2}\right)$$ 
(x - y*(5 - sqrt(29))/2)*(x - y*(5 + sqrt(29))/2)
Numerical answer [src] 
x^2 - y^2 - 5.0*x*y
x^2 - y^2 - 5.0*x*y
Powers [src] 
 2    2        
x  - y  - 5*x*y
$$x^{2} - 5 x y - y^{2}$$ 
x^2 - y^2 - 5*x*y
Common denominator [src] 
 2    2        
x  - y  - 5*x*y
$$x^{2} - 5 x y - y^{2}$$ 
x^2 - y^2 - 5*x*y
Rational denominator [src] 
 2    2        
x  - y  - 5*x*y
$$x^{2} - 5 x y - y^{2}$$ 
x^2 - y^2 - 5*x*y
Trigonometric part [src] 
 2    2        
x  - y  - 5*x*y
$$x^{2} - 5 x y - y^{2}$$ 
x^2 - y^2 - 5*x*y
Combining rational expressions [src] 
 2               
x  + y*(-y - 5*x)
$$x^{2} + y \left(- 5 x - y\right)$$ 
x^2 + y*(-y - 5*x)
Combinatorics [src] 
 2    2        
x  - y  - 5*x*y
$$x^{2} - 5 x y - y^{2}$$ 
x^2 - y^2 - 5*x*y
Assemble expression [src] 
 2    2        
x  - y  - 5*x*y
$$x^{2} - 5 x y - y^{2}$$ 
x^2 - y^2 - 5*x*y
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