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Expression simplification/ Factor perfect squares/ x^2-x*a+12*a^2

Factor x^2-x*a+12*a^2 squared

An expression to simplify:

The solution

You have entered [src] 
 2             2
x  - x*a + 12*a
$$12 a^{2} + \left(- a x + x^{2}\right)$$ 
x^2 - x*a + 12*a^2
General simplification [src] 
 2       2      
x  + 12*a  - a*x
$$12 a^{2} - a x + x^{2}$$ 
x^2 + 12*a^2 - a*x
The perfect square
Let's highlight the perfect square of the square three-member
$$12 a^{2} + \left(- a x + x^{2}\right)$$
Let us write down the identical expression
$$12 a^{2} + \left(- a x + x^{2}\right) = \frac{47 x^{2}}{48} + \left(12 a^{2} - a x + \frac{x^{2}}{48}\right)$$
or
$$12 a^{2} + \left(- a x + x^{2}\right) = \frac{47 x^{2}}{48} + \left(2 \sqrt{3} a - \frac{\sqrt{3} x}{12}\right)^{2}$$
Factorization [src] 
/      /        ____\\ /      /        ____\\
|    x*\1 - I*\/ 47 /| |    x*\1 + I*\/ 47 /|
|a - ----------------|*|a - ----------------|
\           24       / \           24       /
$$\left(a - \frac{x \left(1 - \sqrt{47} i\right)}{24}\right) \left(a - \frac{x \left(1 + \sqrt{47} i\right)}{24}\right)$$ 
(a - x*(1 - i*sqrt(47))/24)*(a - x*(1 + i*sqrt(47))/24)
Numerical answer [src] 
x^2 + 12.0*a^2 - a*x
x^2 + 12.0*a^2 - a*x
Powers [src] 
 2       2      
x  + 12*a  - a*x
$$12 a^{2} - a x + x^{2}$$ 
x^2 + 12*a^2 - a*x
Assemble expression [src] 
 2       2      
x  + 12*a  - a*x
$$12 a^{2} - a x + x^{2}$$ 
x^2 + 12*a^2 - a*x
Trigonometric part [src] 
 2       2      
x  + 12*a  - a*x
$$12 a^{2} - a x + x^{2}$$ 
x^2 + 12*a^2 - a*x
Rational denominator [src] 
 2       2      
x  + 12*a  - a*x
$$12 a^{2} - a x + x^{2}$$ 
x^2 + 12*a^2 - a*x
Combinatorics [src] 
 2       2      
x  + 12*a  - a*x
$$12 a^{2} - a x + x^{2}$$ 
x^2 + 12*a^2 - a*x
Common denominator [src] 
 2       2      
x  + 12*a  - a*x
$$12 a^{2} - a x + x^{2}$$ 
x^2 + 12*a^2 - a*x
Combining rational expressions [src] 
    2            
12*a  + x*(x - a)
$$12 a^{2} + x \left(- a + x\right)$$ 
12*a^2 + x*(x - a)
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