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Expression simplification/ Factor perfect squares/ x^2-x-5

Factor x^2-x-5 squared

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=−214n = - \frac{21}{4}
So,
(x−12)2−214\left(x - \frac{1}{2}\right)^{2} - \frac{21}{4}
Factorization [src] 
/            ____\ /            ____\
|      1   \/ 21 | |      1   \/ 21 |
|x + - - + ------|*|x + - - - ------|
\      2     2   / \      2     2   /
(x+(−12+212))(x+(−212−12))\left(x + \left(- \frac{1}{2} + \frac{\sqrt{21}}{2}\right)\right) \left(x + \left(- \frac{\sqrt{21}}{2} - \frac{1}{2}\right)\right) 
(x - 1/2 + sqrt(21)/2)*(x - 1/2 - sqrt(21)/2)
Powers [src] 
      2    
-5 + x  - x
x2−x−5x^{2} - x - 5 
-5 + x^2 - x
Combinatorics [src] 
      2    
-5 + x  - x
x2−x−5x^{2} - x - 5 
-5 + x^2 - x
Assemble expression [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
Rational denominator [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
Trigonometric part [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)
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