What are the solutions to the equation (x+1)^3-(x-1)=6x(x-3) ?

The solutions to the equation (x+1)^3-(x-1)=6x(x-3) are x\approx-0.09849…

Find the zeros of (x+1)^3-(x-1)=6x(x-3)

The zeros of (x+1)^3-(x-1)=6x(x-3) are x\approx-0.09849…

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(x + 1)^{3} - (x - 1) = 6 x (x - 3)

x \approx - 0.09849 \dots

Solution steps

(x + 1)^{3} - (x - 1) = 6 x (x - 3)

Expand

(x + 1)^{3} - (x - 1) : x^{3} + 3 x^{2} + 2 x + 2

Expand

6 x (x - 3) : 6 x^{2} - 18 x

x^{3} + 3 x^{2} + 2 x + 2 = 6 x^{2} - 18 x

Move

18 x

to the left side

x^{3} + 3 x^{2} + 20 x + 2 = 6 x^{2}

Move

6 x^{2}

to the left side

x^{3} - 3 x^{2} + 20 x + 2 = 0

Find one solution for

x^{3} - 3 x^{2} + 20 x + 2 = 0

using Newton-Raphson:

x \approx - 0.09849 \dots

Apply long division:

\frac{x ^{3} - 3 x ^{2} + 20 x + 2}{x + 0.09849 \dots} = x^{2} - 3.09849 \dots x + 20.30519 \dots

x^{2} - 3.09849 \dots x + 20.30519 \dots \approx 0

Find one solution for

x^{2} - 3.09849 \dots x + 20.30519 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx - 0.09849 \dots

x^{3} - 7 x - 8 = 0

675 = 5 x^{3}

2 x^{3} - 1 - x^{6} + 1 = 0

- x^{3} + 2 x^{2} + 7 x + 2 = 0

1 - 4 z + 4 z^{4} = 0

What are the solutions to the equation (x+1)^3-(x-1)=6x(x-3) ?
The solutions to the equation (x+1)^3-(x-1)=6x(x-3) are x\approx-0.09849…
Find the zeros of (x+1)^3-(x-1)=6x(x-3)
The zeros of (x+1)^3-(x-1)=6x(x-3) are x\approx-0.09849…