Question

Solve for x
e^-2x-2xe^-2x=0

Answer 1

\[e ^{-2x}-2xe ^{-2x}=0\]

Answer 2

Factoring, you have\[e^{-2x}(1-2x)=0\]
What do you know about exponentials?

Answer 3

Very little

Answer 4

I'll narrow it down a bit. For any value of x, what will e^(ax) be?

Answer 5

1

Answer 6

Not quite... That's only true for x = 0. The point I'm trying to get across is that
\[e^{ax}>0 \text{ for any constant a and value of x.}\]

Answer 7

oh ok

Answer 8

Do you see how you can use this fact?