Question 1142356
<pre>
house number = 50

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the work out:

{{{ (x+14) = n^2 }}}
{{{ (x-14) = m^2 }}}


Subtracting:
{{{ 28 = n^2-m^2 = (n-m)(n+m) }}}   n>m;  n,m  integers

28 is 1*28, 2*14, or 4*7

Case 1:
  n-m = 1
  n+m = 28

(adding): 2n = 29   non-integer solution, no good

Case 2:
  n-m = 2
  n+m = 14

   2n = 16  -->  n=8 --> m=6  this solution works

Case 3:
   n-m = 4
   n+m = 7

   2n = 11   non-integer solution, no good

Using case 2, and {{{ x + 14 = n^2}}}:
   {{{ x + 14 = 64 }}}  -->  x = 50

Check using {{{ x-14 = m^2 }}}:
    {{{ x - 14 = 50 - 14 = 36 = 6^2 }}} (ok)