Equation discrepancy ? Here's a (possibly dumb) question I found 
If sqrt(2x-1) = -x , find x

The way to solve it is essentially
Square both sides i.e. 2x-1 = x^2
 => x^2-2x+1 = 0
 => x(x-1)-1(x-1) = 0
 => (x-1)^2 = 0
 => x = 1 

But subbing this back we get  sqrt(2x-1) = 1 ! = -x i.e. -1
Also if  (x-1)^2 = 0 => x=+1 or x=-1 , even then it doesn't solve the problem at some point (sqrt(2x-1) = sqrt(-3) ! = 1)
Is the first question assumption itself wrong? If so how does it resolve to a solid answer? 

when you squared both sides, you generated an extraneous solution (two solutions instead of one)..
...I don't know where you received this problem, but is it possible this is a "trick" type problem? I mean, you could simply flip the sign on both sides...so 
-(sqrt(2x-1)) = x 
hope this helped a little...-
