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No. It refers to quadratic equations of the form (x + n)2 = c where n and c are real values. "Completing the square" solves for values of the x-intercepts (y=0). (see the related link)
I believe it to be 360. Because the minute hand moves around the clock (a circle) once, completing 360 degrees. Infinitely many.
You would convert it to vertex form by completing the square. You can also find the optimum value as optimum value and vertex are the same.
If you aren't dealing with algebra, such as x2+3x+21, then completing the square wont be able to solve the porblem, however if you are using algebra, and you cannot factorise, then completing the square will always work