What are the solutions to the equation x^3+x^2+x=-1/3 ?

The solutions to the equation x^3+x^2+x=-1/3 are x\approx-0.44249…

Find the zeros of x^3+x^2+x=-1/3

The zeros of x^3+x^2+x=-1/3 are x\approx-0.44249…

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x^{3} + x^{2} + x = - \frac{1}{3}

x \approx - 0.44249 \dots

Solution steps

x^{3} + x^{2} + x = - \frac{1}{3}

Multiply both sides by

3

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

Move

1

to the left side

3 x^{3} + 3 x^{2} + 3 x + 1 = 0

Find one solution for

3 x^{3} + 3 x^{2} + 3 x + 1 = 0

using Newton-Raphson:

x \approx - 0.44249 \dots

Apply long division:

\frac{3 x ^{3} + 3 x ^{2} + 3 x + 1}{x + 0.44249 \dots} = 3 x^{2} + 1.67251 \dots x + 2.25992 \dots

3 x^{2} + 1.67251 \dots x + 2.25992 \dots \approx 0

Find one solution for

3 x^{2} + 1.67251 \dots x + 2.25992 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx - 0.44249 \dots

u^{3} - 64 = 0

r^{3} + r^{2} - 23 r - 35 = 0

12 x^{4} + 7 x^{3} + 49 x^{2} + 28 x + 4 = 0

0 = 6 x^{2} + x^{3}

x (x + 2) (x + 3) = - 1

What are the solutions to the equation x^3+x^2+x=-1/3 ?
The solutions to the equation x^3+x^2+x=-1/3 are x\approx-0.44249…
Find the zeros of x^3+x^2+x=-1/3
The zeros of x^3+x^2+x=-1/3 are x\approx-0.44249…