#### Answer

no solution

#### Work Step by Step

Subtracting $2$ to both sides of the equation, the given equation, $
\left(\dfrac{1}{2}\right)^x+2=0
,$ is equivalent to
\begin{array}{l}\require{cancel}
\left(\dfrac{1}{2}\right)^x=-2
.\end{array}
The left side of the equation above is always a positive number for any value of $x$. This will never be equal to the negative value at the right. Hence, this equation does not have a solution.