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Expression simplification/ Factor perfect squares/ x^2-x*b-13*b^2

Factor x^2-x*b-13*b^2 squared

An expression to simplify:

The solution

You have entered [src] 
 2             2
x  - x*b - 13*b
$$- 13 b^{2} + \left(- b x + x^{2}\right)$$ 
x^2 - x*b - 13*b^2
The perfect square
Let's highlight the perfect square of the square three-member
$$- 13 b^{2} + \left(- b x + x^{2}\right)$$
Let us write down the identical expression
$$- 13 b^{2} + \left(- b x + x^{2}\right) = \frac{53 x^{2}}{52} + \left(- 13 b^{2} - b x - \frac{x^{2}}{52}\right)$$
or
$$- 13 b^{2} + \left(- b x + x^{2}\right) = \frac{53 x^{2}}{52} - \left(\sqrt{13} b + \frac{\sqrt{13} x}{26}\right)^{2}$$
General simplification [src] 
 2       2      
x  - 13*b  - b*x
$$- 13 b^{2} - b x + x^{2}$$ 
x^2 - 13*b^2 - b*x
Factorization [src] 
/      /       ____\\ /      /      ____\\
|    x*\-1 + \/ 53 /| |    x*\1 + \/ 53 /|
|b - ---------------|*|b + --------------|
\           26      / \          26      /
$$\left(b - \frac{x \left(-1 + \sqrt{53}\right)}{26}\right) \left(b + \frac{x \left(1 + \sqrt{53}\right)}{26}\right)$$ 
(b - x*(-1 + sqrt(53))/26)*(b + x*(1 + sqrt(53))/26)
Rational denominator [src] 
 2       2      
x  - 13*b  - b*x
$$- 13 b^{2} - b x + x^{2}$$ 
x^2 - 13*b^2 - b*x
Common denominator [src] 
 2       2      
x  - 13*b  - b*x
$$- 13 b^{2} - b x + x^{2}$$ 
x^2 - 13*b^2 - b*x
Combining rational expressions [src] 
      2            
- 13*b  + x*(x - b)
$$- 13 b^{2} + x \left(- b + x\right)$$ 
-13*b^2 + x*(x - b)
Combinatorics [src] 
 2       2      
x  - 13*b  - b*x
$$- 13 b^{2} - b x + x^{2}$$ 
x^2 - 13*b^2 - b*x
Assemble expression [src] 
 2       2      
x  - 13*b  - b*x
$$- 13 b^{2} - b x + x^{2}$$ 
x^2 - 13*b^2 - b*x
Powers [src] 
 2       2      
x  - 13*b  - b*x
$$- 13 b^{2} - b x + x^{2}$$ 
x^2 - 13*b^2 - b*x
Trigonometric part [src] 
 2       2      
x  - 13*b  - b*x
$$- 13 b^{2} - b x + x^{2}$$ 
x^2 - 13*b^2 - b*x
Numerical answer [src] 
x^2 - 13.0*b^2 - b*x
x^2 - 13.0*b^2 - b*x
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