Going through completing the square with algebra gives the quadratic formula if you're not careful. So since completing the square gives an answer in the form of \(\pm \sqrt {y} - z\), we can work off of that to guide us.

\(ax^2 + bx + c = 0 \Rightarrow x^2 + \frac {bx}{a} + \frac {c}{a} = 0\)

\((x + \frac {b}{2a})^2 - \frac {b^2}{4a^2} + \frac {c}{a} = 0\)

\((x + \frac {b}{2a})^2 = \frac {b^2}{4a^2} - \frac {c}{a}\)

\(x + \frac {b}{2a} = \pm \sqrt {\frac {b^2}{4a^2} - \frac {c}{a}}\)

So that means that the formula for completing the square is

\[x = \pm \sqrt {\frac {b^2}{4a^2} - \frac {c}{a}} - \frac {b}{2a}\]

## Comments

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TopNewestWell,actually this \(\textbf{IS}\) the quadratic formula.Just simplify: \[x=\pm\sqrt{\frac{b^2-4ac}{4a^2}}-\frac{b}{2a}\\x=\pm\frac{\sqrt{b^2-4ac}}{2a}-\frac{b}{2a}\\ \boxed{x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}}\] – Abdur Rehman Zahid · 2 years, 3 months ago

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