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Expression simplification/ Factor perfect squares/ -x^2-x*a-8*a^2

Factor -x^2-x*a-8*a^2 squared

An expression to simplify:

The solution

You have entered [src] 
   2            2
- x  - x*a - 8*a
$$- 8 a^{2} + \left(- a x - x^{2}\right)$$ 
-x^2 - x*a - 8*a^2
General simplification [src] 
   2      2      
- x  - 8*a  - a*x
$$- 8 a^{2} - a x - x^{2}$$ 
-x^2 - 8*a^2 - a*x
The perfect square
Let's highlight the perfect square of the square three-member
$$- 8 a^{2} + \left(- a x - x^{2}\right)$$
Let us write down the identical expression
$$- 8 a^{2} + \left(- a x - x^{2}\right) = - \frac{31 x^{2}}{32} + \left(- 8 a^{2} - a x - \frac{x^{2}}{32}\right)$$
or
$$- 8 a^{2} + \left(- a x - x^{2}\right) = - \frac{31 x^{2}}{32} - \left(2 \sqrt{2} a + \frac{\sqrt{2} x}{8}\right)^{2}$$
Factorization [src] 
/      /         ____\\ /      /        ____\\
|    x*\-1 + I*\/ 31 /| |    x*\1 + I*\/ 31 /|
|a - -----------------|*|a + ----------------|
\            16       / \           16       /
$$\left(a - \frac{x \left(-1 + \sqrt{31} i\right)}{16}\right) \left(a + \frac{x \left(1 + \sqrt{31} i\right)}{16}\right)$$ 
(a - x*(-1 + i*sqrt(31))/16)*(a + x*(1 + i*sqrt(31))/16)
Combining rational expressions [src] 
     2             
- 8*a  + x*(-a - x)
$$- 8 a^{2} + x \left(- a - x\right)$$ 
-8*a^2 + x*(-a - x)
Common denominator [src] 
   2      2      
- x  - 8*a  - a*x
$$- 8 a^{2} - a x - x^{2}$$ 
-x^2 - 8*a^2 - a*x
Assemble expression [src] 
   2      2      
- x  - 8*a  - a*x
$$- 8 a^{2} - a x - x^{2}$$ 
-x^2 - 8*a^2 - a*x
Numerical answer [src] 
-x^2 - 8.0*a^2 - a*x
-x^2 - 8.0*a^2 - a*x
Combinatorics [src] 
   2      2      
- x  - 8*a  - a*x
$$- 8 a^{2} - a x - x^{2}$$ 
-x^2 - 8*a^2 - a*x
Trigonometric part [src] 
   2      2      
- x  - 8*a  - a*x
$$- 8 a^{2} - a x - x^{2}$$ 
-x^2 - 8*a^2 - a*x
Rational denominator [src] 
   2      2      
- x  - 8*a  - a*x
$$- 8 a^{2} - a x - x^{2}$$ 
-x^2 - 8*a^2 - a*x
Powers [src] 
   2      2      
- x  - 8*a  - a*x
$$- 8 a^{2} - a x - x^{2}$$ 
-x^2 - 8*a^2 - a*x
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