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Expression simplification/ Factor perfect squares/ y^2+13*y*x-5*x^2

Factor y^2+13*y*x-5*x^2 squared

An expression to simplify:

The solution

You have entered [src] 
 2               2
y  + 13*y*x - 5*x
$$- 5 x^{2} + \left(x 13 y + y^{2}\right)$$ 
y^2 + (13*y)*x - 5*x^2
The perfect square
Let's highlight the perfect square of the square three-member
$$- 5 x^{2} + \left(x 13 y + y^{2}\right)$$
Let us write down the identical expression
$$- 5 x^{2} + \left(x 13 y + y^{2}\right) = \frac{189 y^{2}}{20} + \left(- 5 x^{2} + 13 x y - \frac{169 y^{2}}{20}\right)$$
or
$$- 5 x^{2} + \left(x 13 y + y^{2}\right) = \frac{189 y^{2}}{20} - \left(\sqrt{5} x - \frac{13 \sqrt{5} y}{10}\right)^{2}$$
Factorization [src] 
/      /         ____\\ /      /         ____\\
|    y*\13 - 3*\/ 21 /| |    y*\13 + 3*\/ 21 /|
|x - -----------------|*|x - -----------------|
\            10       / \            10       /
$$\left(x - \frac{y \left(13 - 3 \sqrt{21}\right)}{10}\right) \left(x - \frac{y \left(13 + 3 \sqrt{21}\right)}{10}\right)$$ 
(x - y*(13 - 3*sqrt(21))/10)*(x - y*(13 + 3*sqrt(21))/10)
General simplification [src] 
 2      2         
y  - 5*x  + 13*x*y
$$- 5 x^{2} + 13 x y + y^{2}$$ 
y^2 - 5*x^2 + 13*x*y
Numerical answer [src] 
y^2 - 5.0*x^2 + 13.0*x*y
y^2 - 5.0*x^2 + 13.0*x*y
Powers [src] 
 2      2         
y  - 5*x  + 13*x*y
$$- 5 x^{2} + 13 x y + y^{2}$$ 
y^2 - 5*x^2 + 13*x*y
Assemble expression [src] 
 2      2         
y  - 5*x  + 13*x*y
$$- 5 x^{2} + 13 x y + y^{2}$$ 
y^2 - 5*x^2 + 13*x*y
Combining rational expressions [src] 
     2               
- 5*x  + y*(y + 13*x)
$$- 5 x^{2} + y \left(13 x + y\right)$$ 
-5*x^2 + y*(y + 13*x)
Rational denominator [src] 
 2      2         
y  - 5*x  + 13*x*y
$$- 5 x^{2} + 13 x y + y^{2}$$ 
y^2 - 5*x^2 + 13*x*y
Common denominator [src] 
 2      2         
y  - 5*x  + 13*x*y
$$- 5 x^{2} + 13 x y + y^{2}$$ 
y^2 - 5*x^2 + 13*x*y
Combinatorics [src] 
 2      2         
y  - 5*x  + 13*x*y
$$- 5 x^{2} + 13 x y + y^{2}$$ 
y^2 - 5*x^2 + 13*x*y
Trigonometric part [src] 
 2      2         
y  - 5*x  + 13*x*y
$$- 5 x^{2} + 13 x y + y^{2}$$ 
y^2 - 5*x^2 + 13*x*y
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