Why doesn't the quadratic equation contain $2|a|$ in the denominator? When deriving the quadratic equation as shown in the Wikipedia article about the quadratic equation (current revision) the main proof contains the step:
$$
\left(x+{\frac {b}{2a}}\right)^{2}={\frac {b^{2}-4ac}{4a^{2}}}
$$
the square root is taken from both sides, so why is 
$$\sqrt{4a^2} = 2a$$ 
in the denominator and not
$$ \sqrt{4a^2} = 2\left |a  \right | $$
Could somebody explain this to me? Thank you very much

If you put
$x
=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}
$
into
$ax^2+bx+c$,
since
$x^2
=\dfrac{b^2\mp2b\sqrt{b^2-4ac}+(b^2-4ac)}{4a^2}
=\dfrac{2b^2-4ac\mp2b\sqrt{b^2-4ac}}{4a^2}
$
you get
$\begin{array}\\
ax^2+bx+c
&a\dfrac{2b^2-4ac\mp2b\sqrt{b^2-4ac}}{4a^2}
+b\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}+c\\
&=\dfrac{2b^2-4ac\mp2b\sqrt{b^2-4ac}}{4a}
+\dfrac{-2b^2\pm 2b\sqrt{b^2-4ac}}{4a}+c\\
&=\dfrac{2b^2-4ac\mp2b\sqrt{b^2-4ac}-2b^2\pm 2b\sqrt{b^2-4ac}+4ac}{4a}\\
&=0\\
\end{array}
$
If you use $|a|$,
it won't work
since you can't
combine the terms.
