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?

The classical formula for the quadratic equation is
$$ax^2+bx+c=0\iff x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}.$$
But there are many circumstances where the quadratic coefficient is $1$ and the first degree coefficient has an explicit factor $2$, and it is worth to remember the simplified formula
$$x^2+2bx+c=0\iff x=-b\pm\sqrt{b^2-c}.$$

In your case, $$x=-2\pm\sqrt{2^2-(-1)}.$$
