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Expression simplification/ Factorization polynomials/ x^2-x+5

Factor polynomial x^2-x+5

An expression to simplify:

The solution

You have entered [src] 
 2        
x  - x + 5
(x2−x)+5\left(x^{2} - x\right) + 5 
x^2 - x + 5
General simplification [src] 
     2    
5 + x  - x
x2−x+5x^{2} - x + 5 
5 + x^2 - x
The perfect square
Let's highlight the perfect square of the square three-member
(x2−x)+5\left(x^{2} - x\right) + 5
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=5c = 5
Then
m=−12m = - \frac{1}{2}
n=194n = \frac{19}{4}
So,
(x−12)2+194\left(x - \frac{1}{2}\right)^{2} + \frac{19}{4}
Factorization [src] 
/              ____\ /              ____\
|      1   I*\/ 19 | |      1   I*\/ 19 |
|x + - - + --------|*|x + - - - --------|
\      2      2    / \      2      2    /
(x+(−12−19i2))(x+(−12+19i2))\left(x + \left(- \frac{1}{2} - \frac{\sqrt{19} i}{2}\right)\right) \left(x + \left(- \frac{1}{2} + \frac{\sqrt{19} i}{2}\right)\right) 
(x - 1/2 + i*sqrt(19)/2)*(x - 1/2 - i*sqrt(19)/2)
Rational denominator [src] 
     2    
5 + x  - x
x2−x+5x^{2} - x + 5 
5 + x^2 - x
Combining rational expressions [src] 
5 + x*(-1 + x)
x(x−1)+5x \left(x - 1\right) + 5 
5 + x*(-1 + x)
Combinatorics [src] 
     2    
5 + x  - x
x2−x+5x^{2} - x + 5 
5 + x^2 - x
Common denominator [src] 
     2    
5 + x  - x
x2−x+5x^{2} - x + 5 
5 + x^2 - x
Trigonometric part [src] 
     2    
5 + x  - x
x2−x+5x^{2} - x + 5 
5 + x^2 - x
Powers [src] 
     2    
5 + x  - x
x2−x+5x^{2} - x + 5 
5 + x^2 - x
Numerical answer [src] 
5.0 + x^2 - x
5.0 + x^2 - x
Assemble expression [src] 
     2    
5 + x  - x
x2−x+5x^{2} - x + 5 
5 + x^2 - x
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