What would the value of x be for this root?

2^(2x) + (2^x) + (1/4) = 0

2^x = [-1 (+/-) sqrt{1 - 4*1*(1/4)}]/2

2^x = -1/2

but 2^x can never be negative...

Your method is okay, but your y is restricted.

A simpler way would be to simply graph the thing for several values of b. It is then easy to recognize that the solution is b < 0.

-Dan