What are the solutions to the equation c^{11}=-1-c/2 ?

The solutions to the equation c^{11}=-1-c/2 are c\approx-0.94362…

Find the zeros of c^{11}=-1-c/2

The zeros of c^{11}=-1-c/2 are c\approx-0.94362…

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c^{11} = - 1 - \frac{c}{2}

c \approx - 0.94362 \dots

Solution steps

c^{11} = - 1 - \frac{c}{2}

Multiply both sides by

2

2 c^{11} = - 2 - c

Move

c

to the left side

2 c^{11} + c = - 2

Move

2

to the left side

2 c^{11} + c + 2 = 0

Find one solution for

2 c^{11} + c + 2 = 0

using Newton-Raphson:

c \approx - 0.94362 \dots

Apply long division:

\frac{2 c ^{11} + c + 2}{c + 0.94362 \dots} = 2 c^{10} - 1.88724 \dots c^{9} + 1.78085 \dots c^{8} - 1.68045 \dots c^{7} + 1.58571 \dots c^{6} - 1.49632 \dots c^{5} + 1.41196 \dots c^{4} - 1.33236 \dots c^{3} + 1.25725 \dots c^{2} - 1.18637 \dots c + 2.11948 \dots

2 c^{10} - 1.88724 \dots c^{9} + 1.78085 \dots c^{8} - 1.68045 \dots c^{7} + 1.58571 \dots c^{6} - 1.49632 \dots c^{5} + 1.41196 \dots c^{4} - 1.33236 \dots c^{3} + 1.25725 \dots c^{2} - 1.18637 \dots c + 2.11948 \dots \approx 0

Find one solution for

2 c^{10} - 1.88724 \dots c^{9} + 1.78085 \dots c^{8} - 1.68045 \dots c^{7} + 1.58571 \dots c^{6} - 1.49632 \dots c^{5} + 1.41196 \dots c^{4} - 1.33236 \dots c^{3} + 1.25725 \dots c^{2} - 1.18637 \dots c + 2.11948 \dots = 0

using Newton-Raphson:

No Solution for

c \in R

The solution is

c \approx - 0.94362 \dots

3 x^{6} + x^{3} (2 x^{3} - 1) = 4

(r^{2} + 2 r + 10) 3 r (r + 1) 2 = 0

2 x^{5} - x^{3} + 2 x^{2} - 1 = 0

5 x^{3} - 5 x = 0

k^{4} - 1 = 0

What are the solutions to the equation c^{11}=-1-c/2 ?
The solutions to the equation c^{11}=-1-c/2 are c\approx-0.94362…
Find the zeros of c^{11}=-1-c/2
The zeros of c^{11}=-1-c/2 are c\approx-0.94362…