To express \(2x^2 - 12x + 7\) in the form \(a(x+b)^2 + c\), we start by completing the square:

1. Factor out the coefficient of \(x^2\) from the first two terms:

\(2(x^2 - 6x) + 7\)

2. Complete the square inside the parentheses:

\(x^2 - 6x = (x-3)^2 - 9\)

3. Substitute back into the expression:

\(2((x-3)^2 - 9) + 7\)

4. Distribute the 2 and simplify:

\(2(x-3)^2 - 18 + 7\)

\(2(x-3)^2 - 11\)

Thus, \(a = 2\), \(b = -3\), and \(c = -11\).