7.237. $4 \log _{4}^{2}(-x)+2 \log _{4}\left(x^{2}\right)=-1$.

7.237. $4 \log _{4}^{2}(-x)+2 \log _{4}\left(x^{2}\right)=-1$.
Solution.

Domain of definition: $\left\{\begin{array}{l}-x>0, \\ x^{2}>0\end{array} \Leftrightarrow x<0\right.$.

Since by the domain of definition $x<0$, we have

$4 \log _{4}^{2}(-x)+4 \log _{4}(-x)+1=0 \Leftrightarrow\left(2 \log _{4}(-x)+1\right)^{2}=0 \Leftrightarrow$

$\Leftrightarrow 2 \log _{4}(-x)=-1, \log _{4}(-x)=-\frac{1}{2}$.

From this, $-x=4^{-1 / 2}=\frac{1}{2}, x=-\frac{1}{2}$.

Answer: $-\frac{1}{2}$.