What are the solutions to the equation 0.5g^9+3.5g=11-0.5g ?

The solutions to the equation 0.5g^9+3.5g=11-0.5g are g\approx 1.31183…

Find the zeros of 0.5g^9+3.5g=11-0.5g

The zeros of 0.5g^9+3.5g=11-0.5g are g\approx 1.31183…

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0.5 g^{9} + 3.5 g = 11 - 0.5 g

g \approx 1.31183 \dots

Solution steps

0.5 g^{9} + 3.5 g = 11 - 0.5 g

Multiply both sides by

10

5 g^{9} + 35 g = 110 - 5 g

Move

5 g

to the left side

5 g^{9} + 40 g = 110

Move

110

to the left side

5 g^{9} + 40 g - 110 = 0

Find one solution for

5 g^{9} + 40 g - 110 = 0

using Newton-Raphson:

g \approx 1.31183 \dots

Apply long division:

\frac{5 g ^{9} + 40 g - 110}{g - 1.31183 \dots} = 5 g^{8} + 6.55915 \dots g^{7} + 8.60449 \dots g^{6} + 11.28764 \dots g^{5} + 14.80747 \dots g^{4} + 19.42490 \dots g^{3} + 25.48218 \dots g^{2} + 33.42831 \dots g + 83.85228 \dots

5 g^{8} + 6.55915 \dots g^{7} + 8.60449 \dots g^{6} + 11.28764 \dots g^{5} + 14.80747 \dots g^{4} + 19.42490 \dots g^{3} + 25.48218 \dots g^{2} + 33.42831 \dots g + 83.85228 \dots \approx 0

Find one solution for

5 g^{8} + 6.55915 \dots g^{7} + 8.60449 \dots g^{6} + 11.28764 \dots g^{5} + 14.80747 \dots g^{4} + 19.42490 \dots g^{3} + 25.48218 \dots g^{2} + 33.42831 \dots g + 83.85228 \dots = 0

using Newton-Raphson:

No Solution for

g \in R

The solution is

g \approx 1.31183 \dots

x, x^{2} (x^{3}) = y^{10}

x^{4} + 5 x^{3} + 13 x^{2} + 29 x + 34 = 0

x^{3} - 2 x^{2} + 3 = 3 x^{2} + 5 x - 22

x^{6} + x^{5} - 2 x^{4} = 0

x^{3} + 9 x^{2} + 27 x + 23 = 0

What are the solutions to the equation 0.5g^9+3.5g=11-0.5g ?
The solutions to the equation 0.5g^9+3.5g=11-0.5g are g\approx 1.31183…
Find the zeros of 0.5g^9+3.5g=11-0.5g
The zeros of 0.5g^9+3.5g=11-0.5g are g\approx 1.31183…