Quadratic formula - check my simplificaiton I am trying to solve this equation using the quadratic formula:
$$x^2 + 4x -1 = 0$$
I start by substituting the values into the quadratic formula:
$$x = {-(4) \pm \sqrt {(4)^2 - 4(1)(-1)} \over 2}$$
which becomes
$$x = {-4 \pm \sqrt{20} \over 2}$$
This is the answer the textbook that I am using gives but I would have thought I could have simplified this further to:
$$x = {-4 \pm \sqrt {(5)(2)(2)} \over 2}$$
which becomes
$$x = {-4 \pm 2 \sqrt 5 \over 2}$$
which becomes
$$x = -2 \pm \sqrt 5$$
Am I right and if so, why would the textbook not have simplified it further?

Note that
$$\frac{B+C}{A}=\frac{B}{A}+\frac{C}{A}$$

$$x=\frac{-4\pm 2\sqrt{5}}{2}=\frac{-4}{2}\pm\frac{2\sqrt{5}}{2}=-2\pm\sqrt{5}.$$
