Quadratic formula $x = \frac{- (b +\sqrt{b^2- 4ac})}{ \pm2a}$ In the proof of the quadratic formula
$$x = \frac{- b +\sqrt{b^2- 4ac}}{2a}$$
shouldn't there be $\pm 2a$ instead of $2a$, since both can be  the square root of $4a^2$?

Another way to approach it which does not rely on the study of the sign of $a$:
\begin{align*}
ax^{2} + bx + c = 0 & \Longleftrightarrow 4a^{2}x^{2} + 4abx + 4ac = 0\\\\
& \Longleftrightarrow (4a^{2}x^{2} + 4abx + b^{2}) = b^{2} - 4ac\\\\
& \Longleftrightarrow (2ax + b)^{2} = b^{2} - 4ac\\\\
& \Longleftrightarrow 2ax + b = \pm\sqrt{b^{2} - 4ac}\\\\
& \Longleftrightarrow x = \frac{-b \pm \sqrt{b^{2} - 4ac}}{2a}
\end{align*}
Hopefully this helps!
