Help with "completing the square" with a quadratic please!!!?

Question

Im currently in College precal and I just started today well anyways I pretty much know how to do ...... Factoring,extraction of roots, and quadratic formula. Im just practicing the "completing the square method" to better myself but for some reason I dont get the answer the same in the textbook.

The problem is:
2r^2+10r+11=0

Well this is what ive done so far....
r^2+5r+25/4= -22/4+25/4
(r+10/4)^2= 3/4
but for some reason i end up with...
r= -5/2 +or- Square root of 3/4 as my result

but my pre cal book has it as... r= (-5 +or- square root of 3)/2

What am I doing wrong? Am I not simplifying? Well after my end result I dont know what to do.

Thank you for everyones time.

Answer 1

You did everything correctly. When you reduce 10/4, you get to:
(r + 5/2)² = 3/4

Square both sides and you get:
r + 5/2 = ±sqrt(3/4)

Now subtract 5/2 from both sides and you have:
r = -5/2 ± sqrt(3/4)

All that the book has done is gone a few steps farther:
r = -5/2 ± sqrt(3) / sqrt(4)
r = -5 / 2 ± sqrt(3) / 2
r = [ -5 ± sqrt(3) ] / 2

Answer 2

(r+10/4) should be (r+5/2)
(r+5/2)^2 =3/4 because 5/2 not 10/4 is wht you squared to get 25/4
sqrt both sides
r+5/2=+or- 3/2
-5/2 from both sides
r=-5/2 +or-sqrt 3/2
which is the same thing as the book says!