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 in this case using the quadratic formula is silly, as it is so easy to complete the square (where the quadatic formula comes from):
$$ x^2+4x-1=(x+2)^2-4-1=0\iff (x+2)^2=5\iff x=-2\pm\sqrt 5.$$
