To solve for *x*
by completing the square, we first isolate the terms involving *x*,
to get .
Then add the square of half the __coefficient__ of the *x* term to both sides to get

Note that what we add is
just a __constan__t obtained by squaring half of the coefficient or
multiplier -6, not “half the middle term” as many students seem to remember it.

To repeat: __There is no x in the added term__!

This equation now has a perfect square on the left.

In fact, , so , and .

Of these two solutions only the one with the minus sign meets the extra restriction . Note also that the solution only makes sense for since if , the expression inside the square root is negative and there is no real number whose square is negative so the square root in that case is undefined as a real number.