When Anna realises that it is Coronation day she starts singing and fantasising about meeting "the one". Then she starts dancing with a head and accidentally lets go and throws the head across the room onto a cake.

If Anna is at point \((5,0)\) on the cartesian co-ordinate plane and the cake is at \((-3,0)\), the flight path of the head can be described by the equation:

\[y=-2x^2+bx+c\]

Find the value of \(b+c\)

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