Solve the following equation for x: $$2^{2x + 1} - 9 \times 2^x + 4 = 0$$

Solve the following equation for x: 
    $$2^{2x + 1}  -  9 \times 2^x  +  4  =  0$$

 SOLUTION:  This is a quadratic in $2^x$. 
           $2 (2^x)^2 - 9 (2^x) +4 = 0$ 
         Use a substitution $u=2^x$ and express the equation in terms of $u$.

Therefore:
  $2u^2 - 9u +4 = 0$ 

Factorise to get 
$ ( 2u- 1 )( u - 4 ) = 0 $
$ 2u - 1 = 0$      or     $u - 4 = 0$ 
$ 2u  = 1 $         or     $u = 4$ 
$ u = 1/2$          or     $u=2^2 $

$2^x=2^{-1}$    or     $2^x=2^2$
 

            $\therefore x=-1, 2$