I notice that this problem involves squares and products of two numbers, which makes me think of the identity $(x + y)^2 = x^2 + 2xy + y^2$. If I apply this identity to the given equation, I get $x^2 + 2xy + y^2 = 25$. I also know that $xy = 6$, so I can substitute that into the equation and get $x^2 + 12 + y^2 = 25$. Now I want to isolate $x^2 + y^2$, so I subtract 12 from both sides and get $x^2 + y^2 = 13$.


If $(x + y)^2 = 25$ and $xy = 6$, what is the value of $x^2 + y^2$?