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Popular >

3x^4-2x^3-27245+69x-9x^2=348062x+2

Solution

3 x^{4} - 2 x^{3} - 27245 + 69 x - 9 x^{2} = 348062 x + 2

Solution

x \approx - 0.07829 \dots, x \approx 49.03942 \dots

Solution steps

3 x^{4} - 2 x^{3} - 27245 + 69 x - 9 x^{2} = 348062 x + 2

Move

2

to the left side

3 x^{4} - 2 x^{3} - 9 x^{2} + 69 x - 27247 = 348062 x

Move

348062 x

to the left side

3 x^{4} - 2 x^{3} - 9 x^{2} - 347993 x - 27247 = 0

Find one solution for

3 x^{4} - 2 x^{3} - 9 x^{2} - 347993 x - 27247 = 0

using Newton-Raphson:

x \approx - 0.07829 \dots

Apply long division:

\frac{3 x ^{4} - 2 x ^{3} - 9 x ^{2} - 347993 x - 27247}{x + 0.07829 \dots} = 3 x^{3} - 2.23489 \dots x^{2} - 8.82501 \dots x - 347992.30902 \dots

3 x^{3} - 2.23489 \dots x^{2} - 8.82501 \dots x - 347992.30902 \dots \approx 0

Find one solution for

3 x^{3} - 2.23489 \dots x^{2} - 8.82501 \dots x - 347992.30902 \dots = 0

using Newton-Raphson:

x \approx 49.03942 \dots

Apply long division:

\frac{3 x ^{3} - 2.23489 \dots x ^{2} - 8.82501 \dots x - 347992.30902 \dots}{x - 49.03942 \dots} = 3 x^{2} + 144.88339 \dots x + 7096.17380 \dots

3 x^{2} + 144.88339 \dots x + 7096.17380 \dots \approx 0

Find one solution for

3 x^{2} + 144.88339 \dots x + 7096.17380 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx - 0.07829 \dots, x \approx 49.03942 \dots

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