7.5. Solve the system of equations
$$
\left\{\begin{array}{l}
a^{2}+3 a+1=\frac{b+c}{2}, \\
b^{2}+3 b+1=\frac{a+c}{2}, \\
c^{2}+3 c+1=\frac{a+b}{2} .
\end{array}\right.
$$
7.5. Adding the three equations yields
$$
(a+1)^{2}+(b+1)^{2}+(c+1)^{2}=0 \text {. }
$$

Then \(a=b=c=-1\). This is the unique solution to the system of equations.