What are the solutions to the equation 11x^{10}=15x-9 ?

The solutions to the equation 11x^{10}=15x-9 are x\approx 0.92058…,x\approx 0.60480…

Find the zeros of 11x^{10}=15x-9

The zeros of 11x^{10}=15x-9 are x\approx 0.92058…,x\approx 0.60480…

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11 x^{10} = 15 x - 9

x \approx 0.92058 \dots, x \approx 0.60480 \dots

Solution steps

11 x^{10} = 15 x - 9

Move

9

to the left side

11 x^{10} + 9 = 15 x

Move

15 x

to the left side

11 x^{10} + 9 - 15 x = 0

Write in the standard form

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

11 x^{10} - 15 x + 9 = 0

Find one solution for

11 x^{10} - 15 x + 9 = 0

using Newton-Raphson:

x \approx 0.92058 \dots

Apply long division:

\frac{11 x ^{10} - 15 x + 9}{x - 0.92058 \dots} = 11 x^{9} + 10.12644 \dots x^{8} + 9.32226 \dots x^{7} + 8.58194 \dots x^{6} + 7.90041 \dots x^{5} + 7.27300 \dots x^{4} + 6.69542 \dots x^{3} + 6.16371 \dots x^{2} + 5.67423 \dots x - 9.77638 \dots

11 x^{9} + 10.12644 \dots x^{8} + 9.32226 \dots x^{7} + 8.58194 \dots x^{6} + 7.90041 \dots x^{5} + 7.27300 \dots x^{4} + 6.69542 \dots x^{3} + 6.16371 \dots x^{2} + 5.67423 \dots x - 9.77638 \dots \approx 0

Find one solution for

11 x^{9} + 10.12644 \dots x^{8} + 9.32226 \dots x^{7} + 8.58194 \dots x^{6} + 7.90041 \dots x^{5} + 7.27300 \dots x^{4} + 6.69542 \dots x^{3} + 6.16371 \dots x^{2} + 5.67423 \dots x - 9.77638 \dots = 0

using Newton-Raphson:

x \approx 0.60480 \dots

Apply long division:

\frac{11 x ^{9} + 10.12644 \dots x ^{8} + 9.32226 \dots x ^{7} + 8.58194 \dots x ^{6} + 7.90041 \dots x ^{5} + 7.27300 \dots x ^{4} + 6.69542 \dots x ^{3} + 6.16371 \dots x ^{2} + 5.67423 \dots x - 9.77638 \dots}{x - 0.60480 \dots} = 11 x^{8} + 16.77926 \dots x^{7} + 19.47039 \dots x^{6} + 20.35768 \dots x^{5} + 20.21278 \dots x^{4} + 19.49774 \dots x^{3} + 18.48770 \dots x^{2} + 17.34512 \dots x + 16.16459 \dots

11 x^{8} + 16.77926 \dots x^{7} + 19.47039 \dots x^{6} + 20.35768 \dots x^{5} + 20.21278 \dots x^{4} + 19.49774 \dots x^{3} + 18.48770 \dots x^{2} + 17.34512 \dots x + 16.16459 \dots \approx 0

Find one solution for

11 x^{8} + 16.77926 \dots x^{7} + 19.47039 \dots x^{6} + 20.35768 \dots x^{5} + 20.21278 \dots x^{4} + 19.49774 \dots x^{3} + 18.48770 \dots x^{2} + 17.34512 \dots x + 16.16459 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx 0.92058 \dots, x \approx 0.60480 \dots

x^{6} - 8 x^{3} + 1 = 0

x^{3} - x^{2} - 54 x + 123 = 0

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

x^{3} - 2 x^{2} - 4 x - 7 = 0

x^{3} - x^{2} - 4 x + 7 = x^{2} - 3 x + 5

What are the solutions to the equation 11x^{10}=15x-9 ?
The solutions to the equation 11x^{10}=15x-9 are x\approx 0.92058…,x\approx 0.60480…
Find the zeros of 11x^{10}=15x-9
The zeros of 11x^{10}=15x-9 are x\approx 0.92058…,x\approx 0.60480…