# Thread: [SOLVED] Stuck on the next step

1. ## [SOLVED] Stuck on the next step

Solve $\displaystyle e^{-2x}-3e^{-x}=-2$ for x without using a calculator

Now the first step i did was make it into a quadratic equation
$\displaystyle e^{-2x}-3e^{-x}+2=0$
Then i let $\displaystyle u=e^{-x}$
which gives me $\displaystyle u^{x}-3u+2=0$
now im kinda stuck on the next step becuase of the $\displaystyle u^{x}$ in the equation, not sure if i started of wrong or if im missing something thats right in front of me

2. Multiply by $\displaystyle e^{2x}$ to get $\displaystyle 2e^{2x}-3e^{x}+1=0$.

3. at which point in the problem are you multiplying $\displaystyle e^{2x}$ because i dont see where the $\displaystyle 2e^{2x}$is coming from and the 1 at the end either

4. ## Correction

It's not $\displaystyle u^x$, it's $\displaystyle u^2$ in your last equation.

5. Originally Posted by Plato
Multiply by $\displaystyle e^{2x}$ to get $\displaystyle 2e^{2x}-3e^{x}+1=0$.
You must know basic algebra in order to do calculus.
$\displaystyle e^{-2x}(e^{2x})-3e^{-x}(e^{2x})=-2(e^{2x})$.