What are the solutions to the equation 5x^2+2x^3=441 ?

The solutions to the equation 5x^2+2x^3=441 are x\approx 5.31259…

Find the zeros of 5x^2+2x^3=441

The zeros of 5x^2+2x^3=441 are x\approx 5.31259…

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5 x^{2} + 2 x^{3} = 441

x \approx 5.31259 \dots

Solution steps

5 x^{2} + 2 x^{3} = 441

Move

441

to the left side

5 x^{2} + 2 x^{3} - 441 = 0

Write in the standard form

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

2 x^{3} + 5 x^{2} - 441 = 0

Find one solution for

2 x^{3} + 5 x^{2} - 441 = 0

using Newton-Raphson:

x \approx 5.31259 \dots

Apply long division:

\frac{2 x ^{3} + 5 x ^{2} - 441}{x - 5.31259 \dots} = 2 x^{2} + 15.62518 \dots x + 83.01028 \dots

2 x^{2} + 15.62518 \dots x + 83.01028 \dots \approx 0

Find one solution for

2 x^{2} + 15.62518 \dots x + 83.01028 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 5.31259 \dots

D^{3} - 11 D - 20 = 0

19 - x^{2} x = - 5

4 x^{2} (x + 9) = 0

2^{6} = x^{3}

6 x^{3} + 27 x^{2} - 54 x = 0

What are the solutions to the equation 5x^2+2x^3=441 ?
The solutions to the equation 5x^2+2x^3=441 are x\approx 5.31259…
Find the zeros of 5x^2+2x^3=441
The zeros of 5x^2+2x^3=441 are x\approx 5.31259…