We can simply substitute the right hand side of the first equation into the second equation:

x² + (x + 1)² = 25

This gives:

x² + x² + 2x + 1 = 25

2x² + 2x − 24 = 0

x² + x − 12 = 0

(x + 4)(x − 3) = 0

So x = -4 or x = 3.

This gives our intersecting points to be: (-4, -3) and (3, 4).

Is it correct? The graph of the situation has:

We can see from the graph that our solution is correct.