What are the solutions to the equation x^9=18-2x ?

The solutions to the equation x^9=18-2x are x\approx 1.35396…

Find the zeros of x^9=18-2x

The zeros of x^9=18-2x are x\approx 1.35396…

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x^{9} = 18 - 2 x

x \approx 1.35396 \dots

Solution steps

x^{9} = 18 - 2 x

Move

2 x

to the left side

x^{9} + 2 x = 18

Move

18

to the left side

x^{9} + 2 x - 18 = 0

Find one solution for

x^{9} + 2 x - 18 = 0

using Newton-Raphson:

x \approx 1.35396 \dots

Apply long division:

\frac{x ^{9} + 2 x - 18}{x - 1.35396 \dots} = x^{8} + 1.35396 \dots x^{7} + 1.83322 \dots x^{6} + 2.48211 \dots x^{5} + 3.36069 \dots x^{4} + 4.55026 \dots x^{3} + 6.16090 \dots x^{2} + 8.34164 \dots x + 13.29428 \dots

x^{8} + 1.35396 \dots x^{7} + 1.83322 \dots x^{6} + 2.48211 \dots x^{5} + 3.36069 \dots x^{4} + 4.55026 \dots x^{3} + 6.16090 \dots x^{2} + 8.34164 \dots x + 13.29428 \dots \approx 0

Find one solution for

x^{8} + 1.35396 \dots x^{7} + 1.83322 \dots x^{6} + 2.48211 \dots x^{5} + 3.36069 \dots x^{4} + 4.55026 \dots x^{3} + 6.16090 \dots x^{2} + 8.34164 \dots x + 13.29428 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 1.35396 \dots

2 (x - 3) < 10

\frac{z - 5}{4} = \frac{z}{9}

\frac{- 4 a ^{3} - 20 a ^{2} + 16 a + 80}{a + 2}

w^{2} - 4

\frac{3 ^{2}}{5} x + \frac{5}{6} = 5 x - \frac{125}{3}

What are the solutions to the equation x^9=18-2x ?
The solutions to the equation x^9=18-2x are x\approx 1.35396…
Find the zeros of x^9=18-2x
The zeros of x^9=18-2x are x\approx 1.35396…