Verified answer

knowing that x = r cosß & y = r sinß & r^2 = x^2 + y^2

r = -3cosß ====> times r both sides

r^2 = -3 r cosß ====> replacing the r^2 with x^2 + y^2 & r cosß with x

x^2 + y^2 = -3x

x^2 + 3x +y^2 = 0 ====> completing square

(x^2 + 3x + 9/4) + y^2 = 9/4 ====> dive the 3 /2 and then square it

( x + 3/2 )^2 + y^2 = 9/4 ====> rectangular equation