where do a cubic and a circle intersect? y=x^3, x^2+y^2=9? Descartes' rule of signs and rational zero theorem at least tell me we have a symmetical +- irrational root; what tools do I use next? is sin theta = cos^3 theta going anywhere? x^2 + x^6 - 9 = 0. I have seen a graphical solution, but have no idea which analytical tools to use.