If a + b + c = 8 and ab + ac + bc = -2, what is a^2 + b^2 + c^2?
\(\begin{array}{|rcll|} \hline (a + b + c)^2 &=& a^2+b^2+c^2+2(ab + ac + bc) \\ 8^2 &=& a^2+b^2+c^2+2(-2) \\ 64 &=& a^2+b^2+c^2-4 \\ \mathbf{68} &=& \mathbf{a^2+b^2+c^2} \\ \hline \end{array} \)
