Question 56514
You didn't do anything wrong.  With even roots, you can get extraneous solutions (false solutions) in which you did everything right and got a solution which doesn't check out.  That's why you always have to check your solutions in even root equations, rational equations and log equations.  I think you probably typed in your steps wrong, but I got x=100 also.  And your right, it doesn't check, therefore, this equation has no solution.
Happy Calculating!!!