Question 1018059
What squares do you know or can you find near 289?


{{{system(20^2=400,14^2=196,15^2=3^3*5^2=9*25=225)}}}


Look at squares between  {{{15^2}}} and {{{20^2}}}.
Maybe try  {{{(x+15)(x+15)=289}}}
{{{x^2+30x+225=289}}}
{{{x^2+30x+225-289=0}}}
{{{x^2+30x-64=0}}}
One factorization of 64 is {{{16*4}}} and another is {{{32*2}}}.  This last one looks like it can work.


{{{x^2+30x-64=(x-2)(x+32)=0}}}
Either x=2  OR  x=-32.


The number can be {{{x+2=15+2=17}}}.
Try checking the square of 17...
{{{highlight(17*17=289)}}}.


x=-32 may also work.
{{{15-32=-17}}} and you easily find  {{{(-17)*(-17)=(1)*17^2=289}}}.


{{{highlight(sqrt(289)=0+- 17)}}}.