How do you solve x^ { 3} + 6x ^ { 2} - 36x \leq 216?

Mar 25, 2017

x $\le$6 is the solution.

Explanation:

${x}^{3} + 6 {x}^{2} - 36 x - 216 \le 0$
check by hit and trial, put x=6 we get L.H.S = 0, so (x-6) is a factor of given equation.
now, given can be written as:
x^2(x-6) +12x(x-6)+36(x-6) <=0 rArr (x-6)(x^2+12x+36)<=0 rArr (x-6)((x+6)^2)<=0 rArrx<=6
now use wavy curve method to solve the inequality. if you don't know that than google it.
graph{x<=6 [-10, 10, -5, 5]} #