Find two consecutive integers if the sum of their squares is 1513

Find two consecutive integers if the sum of their squares is 1513

Let the first integer be n. The next consecutive integer is (n + 1).

The sum of their squares is:
n^2 + (n + 1)^2 = 1513
n^2 + n^2 + 2n + 1 = 1513
2n^2 + 2n + 1 = 1513

Subtract 1513 from each side:
2n^2 + 2n - 1512 = 0

We have a quadratic equation. We type this into our search engine and get:
n = (-27, 28)

Let's take the positive solution.
The second integer is: n + 1
28 + 1 = 29