Answer
$x=5,-6$
Work Step by Step
As per given question: $61-x^2=(x+1)^2$
This can be written as: $61-x^2=x^2+2x+1$
or, $2x^2+2x-60=0$
Need to use factorization to solve the quadratic equation .
$2x^2-10x+12x-60=0$
or, $(x-5)(2x+12)=0$
This implies $x-5=0$ and $2x+12=0$
Hence, $x=5,-6$
