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Expression simplification/ Factor perfect squares/ x^2+x-20

Factor x^2+x-20 squared

An expression to simplify:

The solution

You have entered [src] 
 2         
x  + x - 20
$$\left(x^{2} + x\right) - 20$$ 
x^2 + x - 20
General simplification [src] 
           2
-20 + x + x
$$x^{2} + x - 20$$ 
-20 + x + x^2
Factorization [src] 
(x + 5)*(x - 4)
$$\left(x - 4\right) \left(x + 5\right)$$ 
(x + 5)*(x - 4)
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(x^{2} + x\right) - 20$$
To do this, let's use the formula
$$a x^{2} + b x + c = a \left(m + x\right)^{2} + n$$
where
$$m = \frac{b}{2 a}$$
$$n = \frac{4 a c - b^{2}}{4 a}$$
In this case
$$a = 1$$
$$b = 1$$
$$c = -20$$
Then
$$m = \frac{1}{2}$$
$$n = - \frac{81}{4}$$
So,
$$\left(x + \frac{1}{2}\right)^{2} - \frac{81}{4}$$
Rational denominator [src] 
           2
-20 + x + x
$$x^{2} + x - 20$$ 
-20 + x + x^2
Trigonometric part [src] 
           2
-20 + x + x
$$x^{2} + x - 20$$ 
-20 + x + x^2
Combining rational expressions [src] 
-20 + x*(1 + x)
$$x \left(x + 1\right) - 20$$ 
-20 + x*(1 + x)
Assemble expression [src] 
           2
-20 + x + x
$$x^{2} + x - 20$$ 
-20 + x + x^2
Powers [src] 
           2
-20 + x + x
$$x^{2} + x - 20$$ 
-20 + x + x^2
Numerical answer [src] 
-20.0 + x + x^2
-20.0 + x + x^2
Common denominator [src] 
           2
-20 + x + x
$$x^{2} + x - 20$$ 
-20 + x + x^2
Combinatorics [src] 
(-4 + x)*(5 + x)
$$\left(x - 4\right) \left(x + 5\right)$$ 
(-4 + x)*(5 + x)
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