x^2-2x-13=x^2-2x+1-14=(x-1)^2-14=0; so (x-1)^2=14. Take square roots of each side: x-1=+sqrt(14). From this we can write x=1+sqrt(14)=1+3.742 approx. This gives us x=4.742 and -2.742 as the roots.
The Indian method is simplified because the coefficient of the x^2 term is 1, so it's easy to complete the square without going deeper into the Indian method. The way I do it is to halve the x term coefficient and square it. In this case we halve 2 to get 1 then square 1. I could have moved the constant to the right of the equals sign earlier and simply added the 1 to each side, making 13 into 14 and completing the square on the other side. The Indian method is a variation of the method of completing the square, as I've done.