What are the solutions to the equation (x^3)(x+3)=5 ?

The solutions to the equation (x^3)(x+3)=5 are x\approx 1.07092…,x\approx-3.15865…

Find the zeros of (x^3)(x+3)=5

The zeros of (x^3)(x+3)=5 are x\approx 1.07092…,x\approx-3.15865…

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(x^{3}) (x + 3) = 5

x \approx 1.07092 \dots, x \approx - 3.15865 \dots

Solution steps

(x^{3}) (x + 3) = 5

Expand

(x^{3}) (x + 3) : x^{4} + 3 x^{3}

x^{4} + 3 x^{3} = 5

Move

5

to the left side

x^{4} + 3 x^{3} - 5 = 0

Find one solution for

x^{4} + 3 x^{3} - 5 = 0

using Newton-Raphson:

x \approx 1.07092 \dots

Apply long division:

\frac{x ^{4} + 3 x ^{3} - 5}{x - 1.07092 \dots} = x^{3} + 4.07092 \dots x^{2} + 4.35965 \dots x + 4.66886 \dots

x^{3} + 4.07092 \dots x^{2} + 4.35965 \dots x + 4.66886 \dots \approx 0

Find one solution for

x^{3} + 4.07092 \dots x^{2} + 4.35965 \dots x + 4.66886 \dots = 0

using Newton-Raphson:

x \approx - 3.15865 \dots

Apply long division:

\frac{x ^{3} + 4.07092 \dots x ^{2} + 4.35965 \dots x + 4.66886 \dots}{x + 3.15865 \dots} = x^{2} + 0.91226 \dots x + 1.47811 \dots

x^{2} + 0.91226 \dots x + 1.47811 \dots \approx 0

Find one solution for

x^{2} + 0.91226 \dots x + 1.47811 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx 1.07092 \dots, x \approx - 3.15865 \dots

0 = 12 x^{3} - 12 x^{2}

y^{3} + 5 y^{2} - 49 y - 245 = 0

x^{3} + 6 x^{2} - 9 x + 4 = 0

y, y^{3} = x^{3} - 9 x

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

What are the solutions to the equation (x^3)(x+3)=5 ?
The solutions to the equation (x^3)(x+3)=5 are x\approx 1.07092…,x\approx-3.15865…
Find the zeros of (x^3)(x+3)=5
The zeros of (x^3)(x+3)=5 are x\approx 1.07092…,x\approx-3.15865…