Question 324085
{{{x^2+(x+1)^2=613}}}
Complete the square.
{{{x^2+(x^2+2x+1)=613}}}
{{{2x^2+2x+1=613}}}
{{{2(x^2+x)=612}}}
{{{2(x^2+x+1/4)=612+1/2}}}
{{{2(x+1/2)^2=1224/2+1/2}}}
{{{(x+1/2)^2=1225/4}}}
{{{x+1/2=0 +- 35/2}}}
{{{x=-1/2 +- 35/2}}}
{{{x=-36/2=-18}}} and {{{x=34/2=17}}}
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The integers are either -18 and -17 or 17 and 18.