What are the solutions to the equation (9+x^2)*x=3 ?

The solutions to the equation (9+x^2)*x=3 are x\approx 0.32936…

Find the zeros of (9+x^2)*x=3

The zeros of (9+x^2)*x=3 are x\approx 0.32936…

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(9 + x^{2}) \cdot x = 3

x \approx 0.32936 \dots

Solution steps

(9 + x^{2}) x = 3

Expand

(9 + x^{2}) x : 9 x + x^{3}

9 x + x^{3} = 3

Move

3

to the left side

9 x + x^{3} - 3 = 0

Write in the standard form

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

x^{3} + 9 x - 3 = 0

Find one solution for

x^{3} + 9 x - 3 = 0

using Newton-Raphson:

x \approx 0.32936 \dots

Apply long division:

\frac{x ^{3} + 9 x - 3}{x - 0.32936 \dots} = x^{2} + 0.32936 \dots x + 9.10848 \dots

x^{2} + 0.32936 \dots x + 9.10848 \dots \approx 0

Find one solution for

x^{2} + 0.32936 \dots x + 9.10848 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 0.32936 \dots

4 x^{3} + 72 x^{2} + 200 x + 400 = 0

x^{3} - 8 x^{2} + 14 x - 12 = 0

(103) = 10 C^{3}

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

955 = 5 x^{3}

What are the solutions to the equation (9+x^2)*x=3 ?
The solutions to the equation (9+x^2)*x=3 are x\approx 0.32936…
Find the zeros of (9+x^2)*x=3
The zeros of (9+x^2)*x=3 are x\approx 0.32936…