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Expression simplification/ Factor perfect squares/ x^2-x*b+15*b^2

Factor x^2-x*b+15*b^2 squared

An expression to simplify:

The solution

You have entered [src] 
 2             2
x  - x*b + 15*b
$$15 b^{2} + \left(- b x + x^{2}\right)$$ 
x^2 - x*b + 15*b^2
Factorization [src] 
/      /        ____\\ /      /        ____\\
|    x*\1 - I*\/ 59 /| |    x*\1 + I*\/ 59 /|
|b - ----------------|*|b - ----------------|
\           30       / \           30       /
$$\left(b - \frac{x \left(1 - \sqrt{59} i\right)}{30}\right) \left(b - \frac{x \left(1 + \sqrt{59} i\right)}{30}\right)$$ 
(b - x*(1 - i*sqrt(59))/30)*(b - x*(1 + i*sqrt(59))/30)
General simplification [src] 
 2       2      
x  + 15*b  - b*x
$$15 b^{2} - b x + x^{2}$$ 
x^2 + 15*b^2 - b*x
The perfect square
Let's highlight the perfect square of the square three-member
$$15 b^{2} + \left(- b x + x^{2}\right)$$
Let us write down the identical expression
$$15 b^{2} + \left(- b x + x^{2}\right) = \frac{59 x^{2}}{60} + \left(15 b^{2} - b x + \frac{x^{2}}{60}\right)$$
or
$$15 b^{2} + \left(- b x + x^{2}\right) = \frac{59 x^{2}}{60} + \left(\sqrt{15} b - \frac{\sqrt{15} x}{30}\right)^{2}$$
Rational denominator [src] 
 2       2      
x  + 15*b  - b*x
$$15 b^{2} - b x + x^{2}$$ 
x^2 + 15*b^2 - b*x
Combinatorics [src] 
 2       2      
x  + 15*b  - b*x
$$15 b^{2} - b x + x^{2}$$ 
x^2 + 15*b^2 - b*x
Combining rational expressions [src] 
    2            
15*b  + x*(x - b)
$$15 b^{2} + x \left(- b + x\right)$$ 
15*b^2 + x*(x - b)
Trigonometric part [src] 
 2       2      
x  + 15*b  - b*x
$$15 b^{2} - b x + x^{2}$$ 
x^2 + 15*b^2 - b*x
Assemble expression [src] 
 2       2      
x  + 15*b  - b*x
$$15 b^{2} - b x + x^{2}$$ 
x^2 + 15*b^2 - b*x
Common denominator [src] 
 2       2      
x  + 15*b  - b*x
$$15 b^{2} - b x + x^{2}$$ 
x^2 + 15*b^2 - b*x
Numerical answer [src] 
x^2 + 15.0*b^2 - b*x
x^2 + 15.0*b^2 - b*x
Powers [src] 
 2       2      
x  + 15*b  - b*x
$$15 b^{2} - b x + x^{2}$$ 
x^2 + 15*b^2 - b*x
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