What are the solutions to the equation x^5=2+x ?

The solutions to the equation x^5=2+x are x\approx 1.26716…

Find the zeros of x^5=2+x

The zeros of x^5=2+x are x\approx 1.26716…

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Popular >

x^{5} = 2 + x

x \approx 1.26716 \dots

Solution steps

x^{5} = 2 + x

Move

x

to the left side

x^{5} - x = 2

Move

2

to the left side

x^{5} - x - 2 = 0

Find one solution for

x^{5} - x - 2 = 0

using Newton-Raphson:

x \approx 1.26716 \dots

Apply long division:

\frac{x ^{5} - x - 2}{x - 1.26716 \dots} = x^{4} + 1.26716 \dots x^{3} + 1.60571 \dots x^{2} + 2.03471 \dots x + 1.57832 \dots

x^{4} + 1.26716 \dots x^{3} + 1.60571 \dots x^{2} + 2.03471 \dots x + 1.57832 \dots \approx 0

Find one solution for

x^{4} + 1.26716 \dots x^{3} + 1.60571 \dots x^{2} + 2.03471 \dots x + 1.57832 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 1.26716 \dots

- 64 x^{3} + 48 x^{2} - 12 x + 1 = 0

3^{2} = x^{4}

6 x^{3} - 2 x - 1 = 0

x^{3} = 1.5

x^{4} - 49 = 0

What are the solutions to the equation x^5=2+x ?
The solutions to the equation x^5=2+x are x\approx 1.26716…
Find the zeros of x^5=2+x
The zeros of x^5=2+x are x\approx 1.26716…