When the sum of a number plus 3 is squared it is 11 more than the sum of the number plus 2 when squared.

[tex]x-number\\\\
(x+3)^2-11=(x+2)^2\\\\
x^2+2*3*x+3^2-11=x^2+2*2*x+4\\\\
x^2+6x+9-11=x^2+4x+4\ \ |-x^2\\\\6x-2=4x+4\\\\6x-4x=4+2\\\\2x=6\ \ |:2\\\\ x=3
[/tex]