Can You Find A Number That Is 56 Less Than It's Square?

An equation for your number x can be written as   (x - 56) = ±√x   (x - 56)^2 = x    (square both sides)   x^2 - 112x + 3136 = x    (work it out)   x^2 - 113x + 3136 = 0    (subtract x from both sides to get to standard form) This can be solved using the quadratic formula, or by factoring. As it happens, we've seen a similar problem before, so we suspect suitable factors are 49 and 64.   (x-49)(x-64) = 0   x = 49  or  x = 64.

The number could be either 49 or 64.

Check   49 - √49 = 56   49 - (-7) = 56    (note that we must use the negative square root for this to work)    64 - √64 = 56   64 - 8 = 56    (yes)