Re: solve by completing the square
\(\displaystyle A\cdot x^2 \, + B\cdot x \, + \, C = 0\)
\(\displaystyle A\cdot [x^2 \, + \frac{B}{A}\cdot x \, + \, \frac{C}{A}] = 0\)
\(\displaystyle A\cdot [x^2 \, +2\cdot \frac{B}{A}\cdot \frac{1}{2}\cdot x \, + \, \frac{C}{A}] = 0\)
\(\displaystyle A\cdot [x^2 \, +2\cdot \frac{B}{A}\cdot \frac{1}{2}\cdot x \, + \, (\frac{B}{2A})^2 \, - \, (\frac{B}{2A})^2 \, + \, \frac{C}{A}] = 0\)
\(\displaystyle A\cdot [(x \, + \, \frac{B}{2A})^2 \, - \, \frac{B^2 \, - \, 4AC}{4A^2}] = 0\)
and you are done....