Po-Shen Loh's new way of solving quadratic equation Quadratic equation, $ax^2+bx+c=0$ and its solution is quadratic equation, $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ 
Now setting $a=1$ then we have $x^2+bx+c=0$
$$x=\frac{-b\pm \sqrt{b^2-4c}}{2}$$ rewrite as 
$$x=-\frac{b}{2}\pm \sqrt{\left(\frac{b}{2}\right)^2-c}$$ 
In this new video Dr. Loh claims to discover a new way of solving the quadratic equation! How? It is the same as the above formula, by using the quadratic formula, the only thing I see different, is he rewrite it in the above form!
Can someone please explain to me how this is a new way?  

Let us illustrate by example.  Consider the equation
\begin{align}
x^2-2019x-2020 = (x-r_1)(x-r_2) = x^2-(r_1+r_2)x+r_1r_2=0.
\end{align}
The key observation is that the roots $r_1, r_2$ adds up to $2019$, which means the average of $r_1$ and $r_2$ is $\frac{2019}{2}$. Hence the roots have the form $r_\pm = \frac{2019}{2}\pm z$ for some $z$.
Next, it follows
\begin{align}
\frac{(2019)^2}{4}-z^2 = r_1r_2 = -2020 \ \ \implies \ \ z =  \sqrt{\frac{(2019)^2}{4}+2020}.
\end{align}
Thus, we have
\begin{align}
r = \frac{2019}{2}\pm \sqrt{\frac{(2019)^2}{4}+2020}.
\end{align}
The "new" aspect is that the derivation avoids completing the square.
Here's another example
\begin{align}
x^2+212323x+24434 = 0
\end{align}
Again, the roots should have the form
\begin{align}
r_\pm = -\frac{212323}{2}\pm z \ \ \implies \ \ \frac{(212323)^2}{4}- z^2= 24434
\end{align}
which means
\begin{align}
z = \sqrt{\frac{(212323)^2}{4}-24434} \ \ \implies \ \ r_\pm = -\frac{212323}{2}\pm \sqrt{\frac{(212323)^2}{4}-24434}.
\end{align}
