What are the solutions to the equation x^{11}+2/9 x=32 ?

The solutions to the equation x^{11}+2/9 x=32 are x\approx 1.36916…

Find the zeros of x^{11}+2/9 x=32

The zeros of x^{11}+2/9 x=32 are x\approx 1.36916…

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x^{11} + \frac{2}{9} x = 32

x \approx 1.36916 \dots

Solution steps

x^{11} + \frac{2}{9} x = 32

Multiply both sides by

9

9 x^{11} + 2 x = 288

Move

288

to the left side

9 x^{11} + 2 x - 288 = 0

Find one solution for

9 x^{11} + 2 x - 288 = 0

using Newton-Raphson:

x \approx 1.36916 \dots

Apply long division:

\frac{9 x ^{11} + 2 x - 288}{x - 1.36916 \dots} = 9 x^{10} + 12.32245 \dots x^{9} + 16.87142 \dots x^{8} + 23.09970 \dots x^{7} + 31.62722 \dots x^{6} + 43.30276 \dots x^{5} + 59.28847 \dots x^{4} + 81.17548 \dots x^{3} + 111.14234 \dots x^{2} + 152.17179 \dots x + 210.34774 \dots

9 x^{10} + 12.32245 \dots x^{9} + 16.87142 \dots x^{8} + 23.09970 \dots x^{7} + 31.62722 \dots x^{6} + 43.30276 \dots x^{5} + 59.28847 \dots x^{4} + 81.17548 \dots x^{3} + 111.14234 \dots x^{2} + 152.17179 \dots x + 210.34774 \dots \approx 0

Find one solution for

9 x^{10} + 12.32245 \dots x^{9} + 16.87142 \dots x^{8} + 23.09970 \dots x^{7} + 31.62722 \dots x^{6} + 43.30276 \dots x^{5} + 59.28847 \dots x^{4} + 81.17548 \dots x^{3} + 111.14234 \dots x^{2} + 152.17179 \dots x + 210.34774 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 1.36916 \dots

x^{4} + 32 x^{2} + 256 = 0

2 x^{3} + 28 = 4

x^{3} + 7 x^{2} = - 10 x

- A^{3} + 24 A^{2} - 67 A + 64 = 0

20 x^{3} = 45 x

What are the solutions to the equation x^{11}+2/9 x=32 ?
The solutions to the equation x^{11}+2/9 x=32 are x\approx 1.36916…
Find the zeros of x^{11}+2/9 x=32
The zeros of x^{11}+2/9 x=32 are x\approx 1.36916…