how do i complete the square and leave in simple radical form? x squared + 18x - 17=0

The key to completing the square is the fact that

Notice the relationship between the constant term, a², and the coefficient of x, 2a. The constant term is the square of half the coefficient of x. So, for example, if you have x² + 6x you can produce a square by adding (6/2)² = 9; x² + 6x + 9 = (x + 3)².

For a problem like the one you sent, say

You need to add (12/2)² = 36, but then you also have to subtract 36 to maintain the equality. Thus you get

When completing the square you need to ensure that the coefficient of x² is one. Sometimes you may need to force it to be one. For example if you want to complete the square with

you need to write it as

and then add ((1/2)(12/5))² = (6/5)² to get

Cheers,
Penny