When you are asked to complete a sqaure you must end up with something like " (X + something)² + something else = 0 "

If for example you have (X + A)² this gives X²+ 2A.X + A²

You should be able to multiply out brackets

The point of completing the square is to do that in reverse.

With your equation you have:

X² - 3X + 10 = 0

With my example you will notice that I had 'A' inside the bracket, and 2A as the coefficent for X. Conversely you have -3X, so inside the bracket you need -1.5.

(X-1.5)²

However this is not the correct answer. If you were to multiply out that bracket you would end up with a + 2.25 (-1.5x-1.5), instead of the +10 that you want. The solution to this is just put another +7.75 on the end of that.

Hence after completing the square:

X² - 3X + 10 = 0 is the same as (X - 1.5)² + 7.75 = 0

I believe this is correct.

edit : Not quite sure what it means by surd form. I thought that was to do with square roots....