# Mathematical rebus: $x^2+15600=649x$

Which name of a large American city does the following equation represent?

$$x^2+15600=649x$$

• @ghosts I don't find it that surprising, given that it's a pretty dumb riddle with only one posted solution. I'm actually surprised that I got this many upvotes! Jun 28, 2015 at 16:15

The city you are referring to is

Chicago

Solving the quadratic equation gives us $x = 25$ or $x = 624$. Or to put it another way, it's '25 or 6 to 4', a song by the band Chicago.

• To the creator, may I suggest rephrasing the riddle to, "what name of a large American city do the roots of this equation represent"? The answer above doesn't involve solving the equation, but rather finding its roots. To say that the entire equation describes a name is a bit generous.
– bcf
Jun 28, 2015 at 13:17
• @bcf I thought about that, but 1) In this case you are actually finding the solution to an equation (which are the roots of the polynomial $x^2-649x+15600$), and 2) I thought that it would make an already simple puzzle way too easy. Jun 28, 2015 at 16:19