#math trivia for #June15: #167 is x*(x+2)-1 for what value of x?

— Burt Kaliski Jr. (@modulomathy) June 16, 2012

This one is fairly straightforward: If we want x*(x+2)-1 = 167, then we need x and (x+2) to be factors of 168. Given that 168 = 12*14, it follows that x is 12.

We should keep in mind, of course, that quadratic equations generally have two solutions. The other one in this case is x = -14, which works out as (-14)*(-14+2)-1 = (-14)*(-12)-1 = 167.

(Note: Heading back to the “archives” for some unfinished answers …)