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

The solutions to the equation (x-3)/2 =-2x^3 are x\approx 0.81718…

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

The zeros of (x-3)/2 =-2x^3 are x\approx 0.81718…

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\frac{x - 3}{2} = - 2 x^{3}

x \approx 0.81718 \dots

Solution steps

\frac{x - 3}{2} = - 2 x^{3}

Multiply both sides by

2

x - 3 = - 4 x^{3}

Switch sides

- 4 x^{3} = x - 3

Move

3

to the left side

- 4 x^{3} + 3 = x

Move

x

to the left side

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

Write in the standard form

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

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

Find one solution for

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

using Newton-Raphson:

x \approx 0.81718 \dots

Apply long division:

\frac{- 4 x ^{3} - x + 3}{x - 0.81718 \dots} = - 4 x^{2} - 3.26873 \dots x - 3.67114 \dots

- 4 x^{2} - 3.26873 \dots x - 3.67114 \dots \approx 0

Find one solution for

- 4 x^{2} - 3.26873 \dots x - 3.67114 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 0.81718 \dots

9262 + x^{3} = 1

(2 x - 7) (x^{3} - 3) (2 x + 5) = 91

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

x^{9} - x^{5} + x^{4} - 1 = 0

(\frac{x - 1}{3})^{3} = \frac{8}{25}

What are the solutions to the equation (x-3)/2 =-2x^3 ?
The solutions to the equation (x-3)/2 =-2x^3 are x\approx 0.81718…
Find the zeros of (x-3)/2 =-2x^3
The zeros of (x-3)/2 =-2x^3 are x\approx 0.81718…