Question 574550
When you look at {{{x^3 + 6x^2 + 12x + 24 = 0}}}, it may remind you of
{{{(x+2)^3=x^3+6x^2+12x+8}}}, so we could "complete the cube"
{{{x^3 + 6x^2 + 12x + 24 = 0}}} --> {{{x^3 + 6x^2 + 12x = -24}}} --> {{{x^3 + 6x^2 + 12x +8= -24+8}}} --> {{{(x+2)^3=-16}}}
The only real solution is {{{x+2=root(3,16)}}} , so
{{{highlight(x=-2-root(3,16))}}}