Factor:
2x^2-17x-33
and find the extraneous soultion, if there is any.
all work shown (or at least most of it)
!

2x^2-17x-33=0  let's complete the square, add 33 to both sides

2x^2-17x=33  make the leading coefficient equal to one, divide all by 2

x^2-8.5=16.5  halve the linear coefficient, square it, and add that to both sides

x^2-8.5+18.0625=34.5625  now left side is a perfect square

(x-4.25)^2=34.5625  take the square root of both sides

x-4.25=±√34.5625  add 4.25 to both sides

x=4.25±√34.5625 so the factors are:

(x+4.25+√34.5625)(x+4.25-√34.5625)