Answer
$x=\frac{1}{2}$
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Work Step by Step
$e^{-2x}-2xe^{-2x}=0$
$-e^{-x}(-1+2x)=0$
Since $e^{-x}\gt0$ for any $x$ in the domain of $e^{-x}$:
$-1+2x=0$
$2x=1$
$x=\frac{1}{2}$
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