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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}
Factorization [src] 
(x + 3)*(x - 2)
(x−2)(x+3)\left(x - 2\right) \left(x + 3\right) 
(x + 3)*(x - 2)
General simplification [src] 
          2
-6 + x + x
x2+x−6x^{2} + x - 6 
-6 + x + x^2
Rational denominator [src] 
          2
-6 + x + x
x2+x−6x^{2} + x - 6 
-6 + x + x^2
Assemble expression [src] 
          2
-6 + x + x
x2+x−6x^{2} + x - 6 
-6 + x + x^2
Common denominator [src] 
          2
-6 + x + x
x2+x−6x^{2} + x - 6 
-6 + x + x^2
Powers [src] 
          2
-6 + x + x
x2+x−6x^{2} + x - 6 
-6 + x + x^2
Trigonometric part [src] 
          2
-6 + x + x
x2+x−6x^{2} + x - 6 
-6 + x + x^2
Numerical answer [src] 
-6.0 + x + x^2
-6.0 + x + x^2
Combining rational expressions [src] 
-6 + x*(1 + x)
x(x+1)−6x \left(x + 1\right) - 6 
-6 + x*(1 + x)
Combinatorics [src] 
(-2 + x)*(3 + x)
(x−2)(x+3)\left(x - 2\right) \left(x + 3\right) 
(-2 + x)*(3 + x)
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