x^3 + 1 = 0
x = -1
x + 1 = 0
x^3 + 1 = x + 1
ok... dithering further...
x^3 = x * x * x
so:
X^3 - x = (x * x * x) - x = x * x = x^2
ok, so:
if x = -1
then x^3 - x = x^3 -(-1) = x^3 + 1
problem:
if x = -1, then x^2 = 1
whereas
X^3 + 1 = -1 + 1 = 0
0 and 1 do not equate
***
(x-1)(x**2+x+1)=x**3-1
(x+1)(x**2-x+1)=x**3+1
***
okers... dithering YET further...
(x+1)(x^2-x+1)=x^3+1
(x^2-x+1)=(x^3+1)/(x+1)
(x^2-x+1)=x^2+(1/(x+1))
x^2-x^2-x+1=x^2-x^2+(1/(x+1))
-x+1=1/(x+1)
-x=(1/(x+1)) -1
x=-((1/(x+1))-1)
um...
we're solving for "x" right?
Use the quadratic formula or completing the square. (QV)