What are the solutions to the equation (x-3)^3=2x(x^2-1) ?

The solutions to the equation (x-3)^3=2x(x^2-1) are x\approx-11.68063…

Find the zeros of (x-3)^3=2x(x^2-1)

The zeros of (x-3)^3=2x(x^2-1) are x\approx-11.68063…

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(x - 3)^{3} = 2 x (x^{2} - 1)

x \approx - 11.68063 \dots

Solution steps

(x - 3)^{3} = 2 x (x^{2} - 1)

Expand

(x - 3)^{3} : x^{3} - 9 x^{2} + 27 x - 27

Expand

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

x^{3} - 9 x^{2} + 27 x - 27 = 2 x^{3} - 2 x

Move

2 x

to the left side

x^{3} - 9 x^{2} + 29 x - 27 = 2 x^{3}

Move

2 x^{3}

to the left side

- x^{3} - 9 x^{2} + 29 x - 27 = 0

Find one solution for

- x^{3} - 9 x^{2} + 29 x - 27 = 0

using Newton-Raphson:

x \approx - 11.68063 \dots

Apply long division:

\frac{- x ^{3} - 9 x ^{2} + 29 x - 27}{x + 11.68063 \dots} = - x^{2} + 2.68063 \dots x - 2.31151 \dots

- x^{2} + 2.68063 \dots x - 2.31151 \dots \approx 0

Find one solution for

- x^{2} + 2.68063 \dots x - 2.31151 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx - 11.68063 \dots

2 x^{3} - 9 x^{2} + 13 x - 6 = 0

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

1 - (p + 3)^{3} = - 8

(4^{2} - x)^{4} = 16

2 = (\frac{1 + r}{100})^{6}

What are the solutions to the equation (x-3)^3=2x(x^2-1) ?
The solutions to the equation (x-3)^3=2x(x^2-1) are x\approx-11.68063…
Find the zeros of (x-3)^3=2x(x^2-1)
The zeros of (x-3)^3=2x(x^2-1) are x\approx-11.68063…