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If \[3x^2-6x+15=a(x-b)^2+c,\] what is the value of \(a+b+c\)?

If \[\frac{1}{3}x^2+6x+10=\frac{1}{a}(x+b)^2-c,\] what is the value of \(a+b+c\)?

What do we get when we complete the square for

\[-\frac{1}{2}x^2+5x+2?\]

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