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

The solutions to the equation x^3+x=-1 are x\approx-0.68232…

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

The zeros of x^3+x=-1 are x\approx-0.68232…

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x^{3} + x = - 1

x \approx - 0.68232 \dots

Solution steps

x^{3} + x = - 1

Move

1

to the left side

x^{3} + x + 1 = 0

Find one solution for

x^{3} + x + 1 = 0

using Newton-Raphson:

x \approx - 0.68232 \dots

Apply long division:

\frac{x ^{3} + x + 1}{x + 0.68232 \dots} = x^{2} - 0.68232 \dots x + 1.46557 \dots

x^{2} - 0.68232 \dots x + 1.46557 \dots \approx 0

Find one solution for

x^{2} - 0.68232 \dots x + 1.46557 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx - 0.68232 \dots

10 x^{3} + 3 x - 4 = 0

2 x^{3} x^{3} x^{2} = 6144

(2 x + 1)^{2} - (x^{2} + 2) (x^{2} - 2) = 4, x + \frac{1}{4} - 3 = 4

x^{6} - 7 x^{3} + 12 = 0

8 x^{4} - 96 x^{3} + 320 x^{2} + 588 x - 1764 = 0

What are the solutions to the equation x^3+x=-1 ?
The solutions to the equation x^3+x=-1 are x\approx-0.68232…
Find the zeros of x^3+x=-1
The zeros of x^3+x=-1 are x\approx-0.68232…