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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
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
$$15 b^{2} + \left(- b x - x^{2}\right) = - \frac{61 x^{2}}{60} + \left(15 b^{2} - b x + \frac{x^{2}}{60}\right)$$
or
$$15 b^{2} + \left(- b x - x^{2}\right) = - \frac{61 x^{2}}{60} + \left(\sqrt{15} b - \frac{\sqrt{15} x}{30}\right)^{2}$$
in the view of the product
$$\left(- \sqrt{\frac{61}{60}} x + \left(\sqrt{15} b + - \frac{\sqrt{15}}{30} x\right)\right) \left(\sqrt{\frac{61}{60}} x + \left(\sqrt{15} b + - \frac{\sqrt{15}}{30} x\right)\right)$$
$$\left(- \frac{\sqrt{915}}{30} x + \left(\sqrt{15} b + - \frac{\sqrt{15}}{30} x\right)\right) \left(\frac{\sqrt{915}}{30} x + \left(\sqrt{15} b + - \frac{\sqrt{15}}{30} x\right)\right)$$
$$\left(\sqrt{15} b + x \left(- \frac{\sqrt{15}}{30} + \frac{\sqrt{915}}{30}\right)\right) \left(\sqrt{15} b + x \left(- \frac{\sqrt{915}}{30} - \frac{\sqrt{15}}{30}\right)\right)$$
$$\left(\sqrt{15} b + x \left(- \frac{\sqrt{15}}{30} + \frac{\sqrt{915}}{30}\right)\right) \left(\sqrt{15} b + x \left(- \frac{\sqrt{915}}{30} - \frac{\sqrt{15}}{30}\right)\right)$$
Factorization [src] 
/      /      ____\\ /      /      ____\\
|    x*\1 - \/ 61 /| |    x*\1 + \/ 61 /|
|b - --------------|*|b - --------------|
\          30      / \          30      /
$$\left(b - \frac{x \left(1 - \sqrt{61}\right)}{30}\right) \left(b - \frac{x \left(1 + \sqrt{61}\right)}{30}\right)$$ 
(b - x*(1 - sqrt(61))/30)*(b - x*(1 + sqrt(61))/30)
Numerical answer [src] 
-x^2 + 15.0*b^2 - b*x
-x^2 + 15.0*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
Trigonometric part [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*(-b - x)
$$15 b^{2} + x \left(- b - x\right)$$ 
15*b^2 + x*(-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
Common denominator [src] 
   2       2      
- x  + 15*b  - b*x
$$15 b^{2} - b x - x^{2}$$ 
-x^2 + 15*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
Rational denominator [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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