Question

Eighty-five more than the square of a number is the same as the square of the quantity that is 17 less than the number. What is the number?

Answer 1

We can turn this word problem into the following equation:
x^2 + 85 = (x - 17)^2
  x^2 + 85 = x^2 - 34x + 289
           -85                       -85
_______________________
      x^2 = x^2 - 34x + 204                    
     +34x         +34x
_______________________
 x^2 + 34x = x^2 + 204
-x^2             -x^2
____________________
       34x = 204
Divide 34 on both sides
      x = 6.
The number is 6.