What are the application of "completing the square" method?

Question

I am trying to convince my students that "completing the square" method is widely used in mathematics.

Here is my effort, could you add other applications to my list?

1. Finding the maximum or minimum value of $ax^2+bx+c$.
2. Solving quadratic equations $ax^2+bx+c=0$.
3. Finding the characteristic of a conic section (such as center, major/minor axes, radius, etc) $Ax^2+Bx+Cy^2+Dy+E=0$.
4. Evaluating $\int \frac{\mathrm{d}x}{ax^2+bx+c}$.
5. Factorizing polynomial, for example $x^4+64=(x^2-4x+8)(x^2+4x+8)$.
6. Finding inverse Laplace of, for example, $\frac{s+1}{s^2+4s+10}$.