Proving Quadratic Formula purplemath.com explains the quadratic formula. I don't understand the third row in the "Derive the Quadratic Formula by solving $ax^2 + bx + c = 0$." section. How does $\dfrac{b}{2a}$ become $\dfrac{b^2}{4a^2}$?

\begin{align*}
ax^2+bx+c &= 0 \\
ax^2+bx &= -c \\
x^2+\frac{b}{a}x &= -\frac{c}{a} \\
x^2+2x\Bigl(\frac{b}{2a}\Bigr)+\Bigl(\frac{b}{2a}\Bigr)^2-\Bigl(\frac{b}{2a}\Bigr)^2 &= -\frac{c}{a} \\
\Bigl(x+\frac{b}{2a}\Bigr)^2-\frac{b^2}{4a^2} &= -\frac{c}{a} \\
\Bigl(x+\frac{b}{2a}\Bigr)^2 &= \frac{b^2-4ac}{4a^2} \\
x+\frac{b}{2a} &= \frac{\pm\sqrt{b^2-4ac}}{2a} \\
x &= \frac{-b\pm\sqrt{b^2-4ac}}{2a}
\end{align*}
