A circle has eqn x^2 + y^2 + 2x - 6y - 40 = 0. Rewrite in the form (x-a)^2 + (y-b)^2 = d.

The first step will be to rearrange the eqn so that the loose number appears on the RHS and the x and y terms are grouped. After this step the eqn will appear as x² + 2x + y² - 6y = 40. The next step will be to do whats called 'completing the square' with both the x and y coefficients. This involves taking the coefficient halving it, squaring it and then adding this new number to both sides of the equation. Having done this with just the x coefficient the equation will appear as (x²+ 2x +1) + y² - 6y = 40 + 1, having done this with both coefficients the equation will appear as (x²+ 2x +1) + (y²- 6y +9) = 40 + 1 + 9 = 50.The final step is to factorise the two equations. So that the final answer is (x+1)^2 + (y-3)^2 = 50.