What are the solutions to the equation m^{10}+8m=-10m-8 ?

The solutions to the equation m^{10}+8m=-10m-8 are m\approx-0.44446…,m\approx-1.31707…

Find the zeros of m^{10}+8m=-10m-8

The zeros of m^{10}+8m=-10m-8 are m\approx-0.44446…,m\approx-1.31707…

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m^{10} + 8 m = - 10 m - 8

m \approx - 0.44446 \dots, m \approx - 1.31707 \dots

Solution steps

m^{10} + 8 m = - 10 m - 8

Move

8

to the left side

m^{10} + 8 m + 8 = - 10 m

Move

10 m

to the left side

m^{10} + 18 m + 8 = 0

Find one solution for

m^{10} + 18 m + 8 = 0

using Newton-Raphson:

m \approx - 0.44446 \dots

Apply long division:

\frac{m ^{10} + 18 m + 8}{m + 0.44446 \dots} = m^{9} - 0.44446 \dots m^{8} + 0.19754 \dots m^{7} - 0.08780 \dots m^{6} + 0.03902 \dots m^{5} - 0.01734 \dots m^{4} + 0.00770 \dots m^{3} - 0.00342 \dots m^{2} + 0.00152 \dots m + 17.99932 \dots

m^{9} - 0.44446 \dots m^{8} + 0.19754 \dots m^{7} - 0.08780 \dots m^{6} + 0.03902 \dots m^{5} - 0.01734 \dots m^{4} + 0.00770 \dots m^{3} - 0.00342 \dots m^{2} + 0.00152 \dots m + 17.99932 \dots \approx 0

Find one solution for

m^{9} - 0.44446 \dots m^{8} + 0.19754 \dots m^{7} - 0.08780 \dots m^{6} + 0.03902 \dots m^{5} - 0.01734 \dots m^{4} + 0.00770 \dots m^{3} - 0.00342 \dots m^{2} + 0.00152 \dots m + 17.99932 \dots = 0

using Newton-Raphson:

m \approx - 1.31707 \dots

Apply long division:

\frac{m ^{9} - 0.44446 \dots m ^{8} + 0.19754 \dots m ^{7} - 0.08780 \dots m ^{6} + 0.03902 \dots m ^{5} - 0.01734 \dots m ^{4} + 0.00770 \dots m ^{3} - 0.00342 \dots m ^{2} + 0.00152 \dots m + 17.99932 \dots}{m + 1.31707 \dots} = m^{8} - 1.76153 \dots m^{7} + 2.51761 \dots m^{6} - 3.40369 \dots m^{5} + 4.52193 \dots m^{4} - 5.97307 \dots m^{3} + 7.87469 \dots m^{2} - 10.37497 \dots m + 13.66614 \dots

m^{8} - 1.76153 \dots m^{7} + 2.51761 \dots m^{6} - 3.40369 \dots m^{5} + 4.52193 \dots m^{4} - 5.97307 \dots m^{3} + 7.87469 \dots m^{2} - 10.37497 \dots m + 13.66614 \dots \approx 0

Find one solution for

m^{8} - 1.76153 \dots m^{7} + 2.51761 \dots m^{6} - 3.40369 \dots m^{5} + 4.52193 \dots m^{4} - 5.97307 \dots m^{3} + 7.87469 \dots m^{2} - 10.37497 \dots m + 13.66614 \dots = 0

using Newton-Raphson:

No Solution for

m \in R

The solutions are

m \approx - 0.44446 \dots, m \approx - 1.31707 \dots

x^{4} + x - 7 = 0

16 x^{3} - 16 = 0

x^{4} - 8 x^{2} + 16 x^{2} - 4 = x^{2} - 4

x^{3} - 6 x^{2} + 2 x - 12 = 0

y^{2} - 3 = y^{3} + y

What are the solutions to the equation m^{10}+8m=-10m-8 ?
The solutions to the equation m^{10}+8m=-10m-8 are m\approx-0.44446…,m\approx-1.31707…
Find the zeros of m^{10}+8m=-10m-8
The zeros of m^{10}+8m=-10m-8 are m\approx-0.44446…,m\approx-1.31707…