How do you solve for x equation y=x^3 +x+1

Question

How do you solve for x equation y=x^3 +x+1

Answer 1

there are 3 solutions.

using Descartes' rule of signs, there are no positive real solutions and 1 negative real solution, with 2 imginary solutions

x^3 + x + 1

if x=0 , y = 1

if x=-1, y = -1

the negative real solution is somewhere between x= 0 and x = -1

try x =-1/2, then y is still >0

try x =3/4 then y = -75/64 + 1 <0

-3/4 < x < -1/2, x is a little closer to -3/4

try x=-2/3, then y = -8/27 - 2/3 + 1 = -26/27 + 1 = 1/27

x=-2/3 is slightly larger than the real negative solution. but it's the nearest simplest fraction, rounded off