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

Factor x^2+x+2 squared

An expression to simplify:

The solution

You have entered [src] 
 2        
x  + x + 2
$$\left(x^{2} + x\right) + 2$$ 
x^2 + x + 2
Factorization [src] 
/            ___\ /            ___\
|    1   I*\/ 7 | |    1   I*\/ 7 |
|x + - + -------|*|x + - - -------|
\    2      2   / \    2      2   /
$$\left(x + \left(\frac{1}{2} - \frac{\sqrt{7} i}{2}\right)\right) \left(x + \left(\frac{1}{2} + \frac{\sqrt{7} i}{2}\right)\right)$$ 
(x + 1/2 + i*sqrt(7)/2)*(x + 1/2 - i*sqrt(7)/2)
General simplification [src] 
         2
2 + x + x
$$x^{2} + x + 2$$ 
2 + x + x^2
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(x^{2} + x\right) + 2$$
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
$$a = 1$$
$$b = 1$$
$$c = 2$$
Then
$$m = \frac{1}{2}$$
$$n = \frac{7}{4}$$
So,
$$\left(x + \frac{1}{2}\right)^{2} + \frac{7}{4}$$
Trigonometric part [src] 
         2
2 + x + x
$$x^{2} + x + 2$$ 
2 + x + x^2
Combinatorics [src] 
         2
2 + x + x
$$x^{2} + x + 2$$ 
2 + x + x^2
Numerical answer [src] 
2.0 + x + x^2
2.0 + x + x^2
Combining rational expressions [src] 
2 + x*(1 + x)
$$x \left(x + 1\right) + 2$$ 
2 + x*(1 + x)
Common denominator [src] 
         2
2 + x + x
$$x^{2} + x + 2$$ 
2 + x + x^2
Assemble expression [src] 
         2
2 + x + x
$$x^{2} + x + 2$$ 
2 + x + x^2
Powers [src] 
         2
2 + x + x
$$x^{2} + x + 2$$ 
2 + x + x^2
Rational denominator [src] 
         2
2 + x + x
$$x^{2} + x + 2$$ 
2 + x + x^2
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