# [SOLVED] Stuck on the next step

• Feb 3rd 2010, 10:42 AM
vinson24
[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
• Feb 3rd 2010, 10:50 AM
Plato
Multiply by \$\displaystyle e^{2x}\$ to get \$\displaystyle 2e^{2x}-3e^{x}+1=0\$.
• Feb 3rd 2010, 11:01 AM
vinson24
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
• Feb 3rd 2010, 11:03 AM
wonderboy1953
Correction
It's not \$\displaystyle u^x\$, it's \$\displaystyle u^2\$ in your last equation.
• Feb 3rd 2010, 12:04 PM
Plato
Quote:

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})\$.