Example

Solve by completing the square: $\quad x^2+13=6x$

Solution

We start by writing the equation in standard form:

Now we have $a=1$, $b=-6$, and $c=13$. It follows that

Therefore, the completed square is

Now we solve by isolating the square and taking square roots:

Notice that our solutions are complex numbers. In fact, they are complex conjugates of one another.