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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
(x2−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
(x2−x)−6\left(x^{2} - x\right) - 6
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=−6c = -6
Then
m=−12m = - \frac{1}{2}
n=−254n = - \frac{25}{4}
So,
(x−12)2−254\left(x - \frac{1}{2}\right)^{2} - \frac{25}{4}
General simplification [src] 
      2    
-6 + x  - x
x2−x−6x^{2} - x - 6 
-6 + x^2 - x
Factorization [src] 
(x + 2)*(x - 3)
(x−3)(x+2)\left(x - 3\right) \left(x + 2\right) 
(x + 2)*(x - 3)
Combinatorics [src] 
(-3 + x)*(2 + x)
(x−3)(x+2)\left(x - 3\right) \left(x + 2\right) 
(-3 + x)*(2 + x)
Powers [src] 
      2    
-6 + x  - x
x2−x−6x^{2} - x - 6 
-6 + x^2 - x
Assemble expression [src] 
      2    
-6 + x  - x
x2−x−6x^{2} - x - 6 
-6 + x^2 - x
Trigonometric part [src] 
      2    
-6 + x  - x
x2−x−6x^{2} - x - 6 
-6 + x^2 - x
Common denominator [src] 
      2    
-6 + x  - x
x2−x−6x^{2} - x - 6 
-6 + x^2 - x
Rational denominator [src] 
      2    
-6 + x  - x
x2−x−6x^{2} - x - 6 
-6 + x^2 - x
Numerical answer [src] 
-6.0 + x^2 - x
-6.0 + x^2 - x
Combining rational expressions [src] 
-6 + x*(-1 + x)
x(x−1)−6x \left(x - 1\right) - 6 
-6 + x*(-1 + x)
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