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

The solutions to the equation x(2x^2)=-2x^2+x-2 are x\approx-1.66253…

Find the zeros of x(2x^2)=-2x^2+x-2

The zeros of x(2x^2)=-2x^2+x-2 are x\approx-1.66253…

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x (2 x^{2}) = - 2 x^{2} + x - 2

x \approx - 1.66253 \dots

Solution steps

x (2 x^{2}) = - 2 x^{2} + x - 2

Refine

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

Move

2

to the left side

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

Move

x

to the left side

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

Move

2 x^{2}

to the left side

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

Write in the standard form

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

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

Find one solution for

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

using Newton-Raphson:

x \approx - 1.66253 \dots

Apply long division:

\frac{2 x ^{3} + 2 x ^{2} - x + 2}{x + 1.66253 \dots} = 2 x^{2} - 1.32507 \dots x + 1.20298 \dots

2 x^{2} - 1.32507 \dots x + 1.20298 \dots \approx 0

Find one solution for

2 x^{2} - 1.32507 \dots x + 1.20298 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx - 1.66253 \dots

x^{4} = 26 x^{2} - 25

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

x^{6} + 19 x^{3} - 216 = 0

x^{4} + x - 3 = 0

z^{4} + z^{2} + 1 = 0

What are the solutions to the equation x(2x^2)=-2x^2+x-2 ?
The solutions to the equation x(2x^2)=-2x^2+x-2 are x\approx-1.66253…
Find the zeros of x(2x^2)=-2x^2+x-2
The zeros of x(2x^2)=-2x^2+x-2 are x\approx-1.66253…