For what value of c will the circle with equation x^2 + 6x + y^2 - 14y + c = 0 have a radius of length 4?
( x2 + 6x + ... ) + ( y2 - 14y + ... ) = -c
Completing the square: ( x2 + 6x + 9 ) + ( y2 - 14y + 49 ) = -c + 9 + 49
(x + 3)2 + (y - 7)2 = 58 - c
For the radius to equal 4, 58 - c = 16 ---> -c = -42 ---> c = 42