LDL Is Completing the Square

The surface is the quadratic form of the book's matrix A, with rows four, two and two, three. Its level curves on the floor are tilted ellipses.

Complete the square. Four x zero squared plus four x zero x one plus three x one squared equals four times x zero plus half of x one, all squared, plus two x one squared.

The rest of the narration is in the book's Companion.