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? 

Lhs is defined for $x\geq1/2$; for those $x$ the lhs is non-negative whereas the rhs is negative.
Some explanation: squaring is “if” but not “iff”: if $x=5$ then $ x^2=25$, but if $x^2=25$ then $x$ may be $-5$ as well.
