Add all the Equations?

Algebra Level 3

\[\large \begin{cases} a^2+2b=7 \\ b^2+4c=-7 \\ c^2+6a=-14\end{cases} \]

\(a,b\) and \(c\) are real numbers that satisfy the system of equations above. What is the value of \(a^2 + b^2 + c^2\)?

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