Symmetric Matrices & Quadratic Forms · Hard problem

A quadratic form is written using the (non-symmetric) matrix $B=\begin{pmatrix}4&6\\-2&7\end{pmatrix}$, i.e. $q(\mathbf x)=\mathbf x^{T}B\mathbf x$. Since $\mathbf x^{T}B\mathbf x$ depends only on $B$'s SYMMETRIC part (the antisymmetric part always contributes $0$ to a quadratic form), $q$'s true representing matrix is $A=\tfrac12(B+B^{T})$. Find the SMALLER eigenvalue of $A$.