1. The problem statement, all variables and given/known data A smokestack deposits soot on the ground with a concentration inversely proportional to the square of the distance from the stack. With two smokestacks 20 miles apart, the concentration of the combined deposits on the line joining them, at a distance x from one stack, is given by the following equation, where k is a positive constants that depends on the quantity of smoke each stack is emitting. [itex]S=((64k)/(x^2)) + (k/((20-x)^2))[/itex] 2. Relevant equations 3. The attempt at a solution 1st I take the derivative [itex]((-128k(20-x)^3))+2kx^3/(x^3)(20-x)^3))[/itex] Then i look for critical points x^3=0 x=0 20-x=0 x=20 The third one is where i get stuck (-128k(20-x)^3))+2kx^3=0 k(-128(-x^3 + 60x^2 -1200x +8000) + 2x^3)=0 (-128(-x^3 + 60x^2 -1200x +8000) + 2x^3)=0 128x^3-7680x^2 +153600x - 1024000 + 2x^3=0 130x^3-7680x^2 +153600x - 1024000=0 130x^3-7680x^2 +153600x = 1024000 how would I solve for this? It's a bit embarrassing on my part, but I never ran into a situation before where I had to find the root of a cubic function.