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Factor x^2+x-5 squared

An expression to simplify:

The solution

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 2        
x  + x - 5
$$\left(x^{2} + x\right) - 5$$
x^2 + x - 5
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(x^{2} + x\right) - 5$$
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
$$a = 1$$
$$b = 1$$
$$c = -5$$
Then
$$m = \frac{1}{2}$$
$$n = - \frac{21}{4}$$
So,
$$\left(x + \frac{1}{2}\right)^{2} - \frac{21}{4}$$
General simplification [src]
          2
-5 + x + x 
$$x^{2} + x - 5$$
-5 + x + x^2
Factorization [src]
/          ____\ /          ____\
|    1   \/ 21 | |    1   \/ 21 |
|x + - - ------|*|x + - + ------|
\    2     2   / \    2     2   /
$$\left(x + \left(\frac{1}{2} - \frac{\sqrt{21}}{2}\right)\right) \left(x + \left(\frac{1}{2} + \frac{\sqrt{21}}{2}\right)\right)$$
(x + 1/2 - sqrt(21)/2)*(x + 1/2 + sqrt(21)/2)
Combining rational expressions [src]
-5 + x*(1 + x)
$$x \left(x + 1\right) - 5$$
-5 + x*(1 + x)
Combinatorics [src]
          2
-5 + x + x 
$$x^{2} + x - 5$$
-5 + x + x^2
Numerical answer [src]
-5.0 + x + x^2
-5.0 + x + x^2
Powers [src]
          2
-5 + x + x 
$$x^{2} + x - 5$$
-5 + x + x^2
Trigonometric part [src]
          2
-5 + x + x 
$$x^{2} + x - 5$$
-5 + x + x^2
Assemble expression [src]
          2
-5 + x + x 
$$x^{2} + x - 5$$
-5 + x + x^2
Rational denominator [src]
          2
-5 + x + x 
$$x^{2} + x - 5$$
-5 + x + x^2
Common denominator [src]
          2
-5 + x + x 
$$x^{2} + x - 5$$
-5 + x + x^2