What are the solutions to the equation 9x^3-4/5 x^2+x-3=68 ?

The solutions to the equation 9x^3-4/5 x^2+x-3=68 are x\approx 2.00188…

Find the zeros of 9x^3-4/5 x^2+x-3=68

The zeros of 9x^3-4/5 x^2+x-3=68 are x\approx 2.00188…

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9 x^{3} - \frac{4}{5} x^{2} + x - 3 = 68

x \approx 2.00188 \dots

Solution steps

9 x^{3} - \frac{4}{5} x^{2} + x - 3 = 68

Multiply both sides by

5

45 x^{3} - 4 x^{2} + 5 x - 15 = 340

Move

340

to the left side

45 x^{3} - 4 x^{2} + 5 x - 355 = 0

Find one solution for

45 x^{3} - 4 x^{2} + 5 x - 355 = 0

using Newton-Raphson:

x \approx 2.00188 \dots

Apply long division:

\frac{45 x ^{3} - 4 x ^{2} + 5 x - 355}{x - 2.00188 \dots} = 45 x^{2} + 86.08498 \dots x + 177.33254 \dots

45 x^{2} + 86.08498 \dots x + 177.33254 \dots \approx 0

Find one solution for

45 x^{2} + 86.08498 \dots x + 177.33254 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 2.00188 \dots

- 3 x^{3} x = 2

x^{3} - 6 x^{2} + 13 x - 10 = 0

2 y^{3} - 17 y^{2} - 9 y = 0

x^{400} = 9^{1000}

4 x^{4} = 53 x^{2} - 49

What are the solutions to the equation 9x^3-4/5 x^2+x-3=68 ?
The solutions to the equation 9x^3-4/5 x^2+x-3=68 are x\approx 2.00188…
Find the zeros of 9x^3-4/5 x^2+x-3=68
The zeros of 9x^3-4/5 x^2+x-3=68 are x\approx 2.00188…