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Expression simplification/ Factor perfect squares/ -x^2+x-6

Factor -x^2+x-6 squared

An expression to simplify:

The solution

You have entered [src] 
   2        
- x  + x - 6
$$\left(- x^{2} + x\right) - 6$$ 
-x^2 + x - 6
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(- x^{2} + x\right) - 6$$
To do this, let's use the formula
$$a x^{2} + b x + c = a \left(m + x\right)^{2} + n$$
where
$$m = \frac{b}{2 a}$$
$$n = \frac{4 a c - b^{2}}{4 a}$$
In this case
$$a = -1$$
$$b = 1$$
$$c = -6$$
Then
$$m = - \frac{1}{2}$$
$$n = - \frac{23}{4}$$
So,
$$- \left(x - \frac{1}{2}\right)^{2} - \frac{23}{4}$$
General simplification [src] 
          2
-6 + x - x
$$- x^{2} + x - 6$$ 
-6 + x - x^2
Factorization [src] 
/              ____\ /              ____\
|      1   I*\/ 23 | |      1   I*\/ 23 |
|x + - - + --------|*|x + - - - --------|
\      2      2    / \      2      2    /
$$\left(x + \left(- \frac{1}{2} - \frac{\sqrt{23} i}{2}\right)\right) \left(x + \left(- \frac{1}{2} + \frac{\sqrt{23} i}{2}\right)\right)$$ 
(x - 1/2 + i*sqrt(23)/2)*(x - 1/2 - i*sqrt(23)/2)
Trigonometric part [src] 
          2
-6 + x - x
$$- x^{2} + x - 6$$ 
-6 + x - x^2
Rational denominator [src] 
          2
-6 + x - x
$$- x^{2} + x - 6$$ 
-6 + x - x^2
Assemble expression [src] 
          2
-6 + x - x
$$- x^{2} + x - 6$$ 
-6 + x - x^2
Combining rational expressions [src] 
-6 + x*(1 - x)
$$x \left(1 - x\right) - 6$$ 
-6 + x*(1 - x)
Numerical answer [src] 
-6.0 + x - x^2
-6.0 + x - x^2
Combinatorics [src] 
          2
-6 + x - x
$$- x^{2} + x - 6$$ 
-6 + x - x^2
Powers [src] 
          2
-6 + x - x
$$- x^{2} + x - 6$$ 
-6 + x - x^2
Common denominator [src] 
          2
-6 + x - x
$$- x^{2} + x - 6$$ 
-6 + x - x^2
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