R2+2r-33=0 solve by completing the square

R^2+2r-33=0 move constant to other side by adding 33 to both sides

r^2+2r=33 halve the linear coefficient, square it and add to both sides, in this case it is just one

r^2+2r+1=34 now the left side is a perfect square ...

(r+1) ^2=34 take the square root of both sides ...

r+1=34^ (1/2) subtract 1 from both sides

r=-1+34^ (1/2) and - 1-34^ (1/2)