What are the solutions to the equation 6c^5+4c^3=2 ?

The solutions to the equation 6c^5+4c^3=2 are c\approx 0.66884…

Find the zeros of 6c^5+4c^3=2

The zeros of 6c^5+4c^3=2 are c\approx 0.66884…

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6 c^{5} + 4 c^{3} = 2

c \approx 0.66884 \dots

Solution steps

6 c^{5} + 4 c^{3} = 2

Move

2

to the left side

6 c^{5} + 4 c^{3} - 2 = 0

Find one solution for

6 c^{5} + 4 c^{3} - 2 = 0

using Newton-Raphson:

c \approx 0.66884 \dots

Apply long division:

\frac{6 c ^{5} + 4 c ^{3} - 2}{c - 0.66884 \dots} = 6 c^{4} + 4.01309 \dots c^{3} + 6.68415 \dots c^{2} + 4.47068 \dots c + 2.99021 \dots

6 c^{4} + 4.01309 \dots c^{3} + 6.68415 \dots c^{2} + 4.47068 \dots c + 2.99021 \dots \approx 0

Find one solution for

6 c^{4} + 4.01309 \dots c^{3} + 6.68415 \dots c^{2} + 4.47068 \dots c + 2.99021 \dots = 0

using Newton-Raphson:

No Solution for

c \in R

The solution is

c \approx 0.66884 \dots

x^{5} - 14 x^{4} + 49 x^{3} = 0

12 x^{3} - 54 x = 0

n^{10} = 42

x (x^{2} - 11) (x^{2} + 49) = 0

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

What are the solutions to the equation 6c^5+4c^3=2 ?
The solutions to the equation 6c^5+4c^3=2 are c\approx 0.66884…
Find the zeros of 6c^5+4c^3=2
The zeros of 6c^5+4c^3=2 are c\approx 0.66884…