What are the solutions to the equation 1-6x^2x=1x-8x^2 ?

The solutions to the equation 1-6x^2x=1x-8x^2 are x\approx 1.30355…

Find the zeros of 1-6x^2x=1x-8x^2

The zeros of 1-6x^2x=1x-8x^2 are x\approx 1.30355…

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1 - 6 x^{2} x = 1 x - 8 x^{2}

x \approx 1.30355 \dots

Solution steps

1 - 6 x^{2} x = 1 \cdot x - 8 x^{2}

Expand

1 - 6 x^{2} x : 1 - 6 x^{3}

1 - 6 x^{3} = x - 8 x^{2}

Move

8 x^{2}

to the left side

1 - 6 x^{3} + 8 x^{2} = x

Move

x

to the left side

1 - 6 x^{3} + 8 x^{2} - x = 0

Write in the standard form

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

- 6 x^{3} + 8 x^{2} - x + 1 = 0

Find one solution for

- 6 x^{3} + 8 x^{2} - x + 1 = 0

using Newton-Raphson:

x \approx 1.30355 \dots

Apply long division:

\frac{- 6 x ^{3} + 8 x ^{2} - x + 1}{x - 1.30355 \dots} = - 6 x^{2} + 0.17864 \dots x - 0.76713 \dots

- 6 x^{2} + 0.17864 \dots x - 0.76713 \dots \approx 0

Find one solution for

- 6 x^{2} + 0.17864 \dots x - 0.76713 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 1.30355 \dots

4 x^{3} + 4 x = 0

4 x^{3} - 8 = 0

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

x^{3} + 2 x^{2} + 10 x = 0

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

What are the solutions to the equation 1-6x^2x=1x-8x^2 ?
The solutions to the equation 1-6x^2x=1x-8x^2 are x\approx 1.30355…
Find the zeros of 1-6x^2x=1x-8x^2
The zeros of 1-6x^2x=1x-8x^2 are x\approx 1.30355…