Consider any complete signed graph $($on any number of nodes$)$ that is not balanced; i$.$e$.$ it contains at least one unbalanced triangle. $($A complete signed graph is a graph in which there is an edge between each pair of nodes, and each edge is labeled with either $+$ or $.)$ A new node X wants to join this network, by attaching to each node using a positive or negative edge. When, if ever, is it possible for X to do this in such a way that it does not become involved in any unbalanced triangles? Give an explanation for your answer.