Solve x3+x^2+x+1=0

$$x3+ { x }^{ 2 } +x+1 = 0$$

Solve for x_3

$$x_{3}=-\left(x^{2}+x+1\right)$$

Solution Steps

Subtract x^{2} from both sides. Anything subtracted from zero gives its negation.

$$x_{3}+x+1=-x^{2}$$

Subtract x from both sides.

$$x_{3}+1=-x^{2}-x$$

Subtract 1 from both sides.

$$x_{3}=-x^{2}-x-1$$

Solve for x (complex solution)

$$x=\frac{\sqrt{-4x_{3}-3}-1}{2}$$

$$x=\frac{-\sqrt{-4x_{3}-3}-1}{2}$$

Solve for x

$$x=\frac{\sqrt{-4x_{3}-3}-1}{2}$$

$$x=\frac{-\sqrt{-4x_{3}-3}-1}{2}\text{, }x_{3}\leq -\frac{3}{4}$$