Quadric Error seems to be only for triangle meshes, is there a similar algorithm for other types of meshes?

Shouldn't the cost for the optimal point x be (x^T)K_{ij}(x) instead of K_{ij}(x)?

Quadric Error seems to be only for triangle meshes, is there a similar algorithm for other types of meshes?

Shouldn't the cost for the optimal point x be (x^T)K_{ij}(x) instead of K_{ij}(x)?