What are the solutions to the equation 5x^9-x^2+2x-3=7 ?

The solutions to the equation 5x^9-x^2+2x-3=7 are x\approx 1.06754…

Find the zeros of 5x^9-x^2+2x-3=7

The zeros of 5x^9-x^2+2x-3=7 are x\approx 1.06754…

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5 x^{9} - x^{2} + 2 x - 3 = 7

x \approx 1.06754 \dots

Solution steps

5 x^{9} - x^{2} + 2 x - 3 = 7

Move

7

to the left side

5 x^{9} - x^{2} + 2 x - 10 = 0

Find one solution for

5 x^{9} - x^{2} + 2 x - 10 = 0

using Newton-Raphson:

x \approx 1.06754 \dots

Apply long division:

\frac{5 x ^{9} - x ^{2} + 2 x - 10}{x - 1.06754 \dots} = 5 x^{8} + 5.33774 \dots x^{7} + 5.69831 \dots x^{6} + 6.08322 \dots x^{5} + 6.49414 \dots x^{4} + 6.93282 \dots x^{3} + 7.40113 \dots x^{2} + 6.90108 \dots x + 9.36724 \dots

5 x^{8} + 5.33774 \dots x^{7} + 5.69831 \dots x^{6} + 6.08322 \dots x^{5} + 6.49414 \dots x^{4} + 6.93282 \dots x^{3} + 7.40113 \dots x^{2} + 6.90108 \dots x + 9.36724 \dots \approx 0

Find one solution for

5 x^{8} + 5.33774 \dots x^{7} + 5.69831 \dots x^{6} + 6.08322 \dots x^{5} + 6.49414 \dots x^{4} + 6.93282 \dots x^{3} + 7.40113 \dots x^{2} + 6.90108 \dots x + 9.36724 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 1.06754 \dots

x^{3} = 6 x

16 x^{4} + 12 x^{2} - 4 x = 0

3 x^{3} - 24 = 0

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

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

What are the solutions to the equation 5x^9-x^2+2x-3=7 ?
The solutions to the equation 5x^9-x^2+2x-3=7 are x\approx 1.06754…
Find the zeros of 5x^9-x^2+2x-3=7
The zeros of 5x^9-x^2+2x-3=7 are x\approx 1.06754…