What are the solutions to the equation 2x^2(x+1)-x+1=0 ?

The solutions to the equation 2x^2(x+1)-x+1=0 are x\approx-1.53697…

Find the zeros of 2x^2(x+1)-x+1=0

The zeros of 2x^2(x+1)-x+1=0 are x\approx-1.53697…

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2 x^{2} (x + 1) - x + 1 = 0

x \approx - 1.53697 \dots

Solution steps

2 x^{2} (x + 1) - x + 1 = 0

Expand

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

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

Find one solution for

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

using Newton-Raphson:

x \approx - 1.53697 \dots

Apply long division:

\frac{2 x ^{3} + 2 x ^{2} - x + 1}{x + 1.53697 \dots} = 2 x^{2} - 1.07394 \dots x + 0.65062 \dots

2 x^{2} - 1.07394 \dots x + 0.65062 \dots \approx 0

Find one solution for

2 x^{2} - 1.07394 \dots x + 0.65062 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx - 1.53697 \dots

2 x^{2} x^{4} x^{4} = 512

(x - 4)^{3} = (\frac{1}{8})^{- 1}

(x - 2) (x + 3) (x - 5) = 0

x^{5} - 10 x^{3} + 9 x = 0

p^{6} = 6

What are the solutions to the equation 2x^2(x+1)-x+1=0 ?
The solutions to the equation 2x^2(x+1)-x+1=0 are x\approx-1.53697…
Find the zeros of 2x^2(x+1)-x+1=0
The zeros of 2x^2(x+1)-x+1=0 are x\approx-1.53697…