Question 63540
You are right on target!!!! Good work!!  I'll pick up where you left off.

x^2-x=-5  Now we are going to make a perfect square out of the left side of the equation.  To do this, we take half of the "B" term as you indicated (which is 1 , square it (we'll get (1/2)^2 and add it to both sides.  This will give us:

x2-x+1/4=-5+1/4 and we have
(x-1/2)^2=-19/4  Take sqrt of both sides:

x-1/2=+or-(i(sqrt19))/2 and 
x=(1+or-i(sqrt19))/2

I'll get you started on this one.  I don't think you will need too much help.
(1)  x^2+xy+y^2=12
(2)  x+y=2 

First, lets rearrange (1) and we have:
  x^2+y(x+y)=12
We see from (2), x+y=2 so lets plug that in (1)
Now we have:
(1a)  x^2+2y=12
but y=2-x. Now lets plug that in (1a)
  x^2+2(2-x)=12 or
  x^2+4-2x=12 simplifying
  x^2-2x-8=0 and we can factor this:
  (x-4)(x+2)=0

I think that you can take it from here.

Hope this helps.  Have a nice holiday----ptaylor