What are the solutions to the equation 5893x^5+0.02x=1.8 ?

The solutions to the equation 5893x^5+0.02x=1.8 are x\approx 0.19805…

Find the zeros of 5893x^5+0.02x=1.8

The zeros of 5893x^5+0.02x=1.8 are x\approx 0.19805…

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5893 x^{5} + 0.02 x = 1.8

x \approx 0.19805 \dots

Solution steps

5893 x^{5} + 0.02 x = 1.8

Multiply both sides by

100

589300 x^{5} + 2 x = 180

Move

180

to the left side

589300 x^{5} + 2 x - 180 = 0

Find one solution for

589300 x^{5} + 2 x - 180 = 0

using Newton-Raphson:

x \approx 0.19805 \dots

Apply long division:

\frac{589300 x ^{5} + 2 x - 180}{x - 0.19805 \dots} = 589300 x^{4} + 116716.51085 \dots x^{3} + 23116.82318 \dots x^{2} + 4578.50830 \dots x + 908.81743 \dots

589300 x^{4} + 116716.51085 \dots x^{3} + 23116.82318 \dots x^{2} + 4578.50830 \dots x + 908.81743 \dots \approx 0

Find one solution for

589300 x^{4} + 116716.51085 \dots x^{3} + 23116.82318 \dots x^{2} + 4578.50830 \dots x + 908.81743 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 0.19805 \dots

x^{4} - 8 = 0

x^{3} - 3 x^{2} - 10 x = 0

4 x^{3} + 6 x^{2} + 4 x - 4 = 0

x^{3} = - 4

x^{3} = 11

What are the solutions to the equation 5893x^5+0.02x=1.8 ?
The solutions to the equation 5893x^5+0.02x=1.8 are x\approx 0.19805…
Find the zeros of 5893x^5+0.02x=1.8
The zeros of 5893x^5+0.02x=1.8 are x\approx 0.19805…