First, we multiply both sides by 2x to isolate the sqrt(x). We are then left with:
-1/sqrt(x) = -x
We can also multiply by (-1) to cancel out the negative on both sides. We can then square both sides to get:
1/x = x^2
Multiplying both sides by x yields:
1 = x^3
So, x = 1. You can check the solution to verify that x = 1 solves the equation.