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

The solutions to the equation x=x^3+1 are x\approx-1.32471…

Find the zeros of x=x^3+1

The zeros of x=x^3+1 are x\approx-1.32471…

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x = x^{3} + 1

x \approx - 1.32471 \dots

Solution steps

x = x^{3} + 1

Switch sides

x^{3} + 1 = x

Move

x

to the left side

x^{3} + 1 - x = 0

Write in the standard form

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

x^{3} - x + 1 = 0

Find one solution for

x^{3} - x + 1 = 0

using Newton-Raphson:

x \approx - 1.32471 \dots

Apply long division:

\frac{x ^{3} - x + 1}{x + 1.32471 \dots} = x^{2} - 1.32471 \dots x + 0.75487 \dots

x^{2} - 1.32471 \dots x + 0.75487 \dots \approx 0

Find one solution for

x^{2} - 1.32471 \dots x + 0.75487 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx - 1.32471 \dots

12 x^{3} = - 3 x^{2} - 12

\frac{256}{3125} x^{5} = 1

4 c^{3} + 24 c^{2} - 64 c = 0

x^{2} - 6 x = 2 x^{2} x

- a^{3} + 6 a^{2} + 15 a + 8 = 0

What are the solutions to the equation x=x^3+1 ?
The solutions to the equation x=x^3+1 are x\approx-1.32471…
Find the zeros of x=x^3+1
The zeros of x=x^3+1 are x\approx-1.32471…