What are the solutions to the equation x^{10}x+8=6x-4 ?

The solutions to the equation x^{10}x+8=6x-4 are x\approx-1.31227…

Find the zeros of x^{10}x+8=6x-4

The zeros of x^{10}x+8=6x-4 are x\approx-1.31227…

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x^{10} x + 8 = 6 x - 4

x \approx - 1.31227 \dots

Solution steps

x^{10} x + 8 = 6 x - 4

Expand

x^{10} x + 8 : x^{11} + 8

x^{11} + 8 = 6 x - 4

Move

4

to the left side

x^{11} + 12 = 6 x

Move

6 x

to the left side

x^{11} + 12 - 6 x = 0

Write in the standard form

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

x^{11} - 6 x + 12 = 0

Find one solution for

x^{11} - 6 x + 12 = 0

using Newton-Raphson:

x \approx - 1.31227 \dots

Apply long division:

\frac{x ^{11} - 6 x + 12}{x + 1.31227 \dots} = x^{10} - 1.31227 \dots x^{9} + 1.72206 \dots x^{8} - 2.25982 \dots x^{7} + 2.96552 \dots x^{6} - 3.89158 \dots x^{5} + 5.10683 \dots x^{4} - 6.70157 \dots x^{3} + 8.79431 \dots x^{2} - 11.54057 \dots x + 9.14441 \dots

x^{10} - 1.31227 \dots x^{9} + 1.72206 \dots x^{8} - 2.25982 \dots x^{7} + 2.96552 \dots x^{6} - 3.89158 \dots x^{5} + 5.10683 \dots x^{4} - 6.70157 \dots x^{3} + 8.79431 \dots x^{2} - 11.54057 \dots x + 9.14441 \dots \approx 0

Find one solution for

x^{10} - 1.31227 \dots x^{9} + 1.72206 \dots x^{8} - 2.25982 \dots x^{7} + 2.96552 \dots x^{6} - 3.89158 \dots x^{5} + 5.10683 \dots x^{4} - 6.70157 \dots x^{3} + 8.79431 \dots x^{2} - 11.54057 \dots x + 9.14441 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx - 1.31227 \dots

3 x^{3} - 8 x^{2} - 19 x + 37 = 0

2 x^{5} - 32 x = 0

4 x^{3} - 12 x^{2} + 16 = 0

x^{2} (4 x - 3) (5 x - 1) = 0

x^{8} = 1 0^{72}

What are the solutions to the equation x^{10}x+8=6x-4 ?
The solutions to the equation x^{10}x+8=6x-4 are x\approx-1.31227…
Find the zeros of x^{10}x+8=6x-4
The zeros of x^{10}x+8=6x-4 are x\approx-1.31227…