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 constant 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.