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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
(x2−x)+2\left(x^{2} - x\right) + 2 
x^2 - x + 2
General simplification [src] 
     2    
2 + x  - x
x2−x+2x^{2} - x + 2 
2 + x^2 - x
Factorization [src] 
/              ___\ /              ___\
|      1   I*\/ 7 | |      1   I*\/ 7 |
|x + - - + -------|*|x + - - - -------|
\      2      2   / \      2      2   /
(x+(−12−7i2))(x+(−12+7i2))\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)
The perfect square
Let's highlight the perfect square of the square three-member
(x2−x)+2\left(x^{2} - x\right) + 2
To do this, let's use the formula
ax2+bx+c=a(m+x)2+na x^{2} + b x + c = a \left(m + x\right)^{2} + n
where
m=b2am = \frac{b}{2 a}
n=4ac−b24an = \frac{4 a c - b^{2}}{4 a}
In this case
a=1a = 1
b=−1b = -1
c=2c = 2
Then
m=−12m = - \frac{1}{2}
n=74n = \frac{7}{4}
So,
(x−12)2+74\left(x - \frac{1}{2}\right)^{2} + \frac{7}{4}
Combining rational expressions [src] 
2 + x*(-1 + x)
x(x−1)+2x \left(x - 1\right) + 2 
2 + x*(-1 + x)
Powers [src] 
     2    
2 + x  - x
x2−x+2x^{2} - x + 2 
2 + x^2 - x
Combinatorics [src] 
     2    
2 + x  - x
x2−x+2x^{2} - x + 2 
2 + x^2 - x
Numerical answer [src] 
2.0 + x^2 - x
2.0 + x^2 - x
Rational denominator [src] 
     2    
2 + x  - x
x2−x+2x^{2} - x + 2 
2 + x^2 - x
Trigonometric part [src] 
     2    
2 + x  - x
x2−x+2x^{2} - x + 2 
2 + x^2 - x
Assemble expression [src] 
     2    
2 + x  - x
x2−x+2x^{2} - x + 2 
2 + x^2 - x
Common denominator [src] 
     2    
2 + x  - x
x2−x+2x^{2} - x + 2 
2 + x^2 - x
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