Summary: Let \(A\) be a noetherian local commutative ring and let \(M\) be a suitable complex of \(A\)-modules. It is proved that \(M\) is a dualizing complex for \(A\) if and only if the trivial extension \(A \ltimes M\) is a Gorenstein differential graded algebra. As a corollary, \(A\) has a dualizing complex if and only if it is a quotient of a Gorenstein local differential graded algebra.