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

The solutions to the equation 2x^2(x-1)=2 are x\approx 1.46557…

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

The zeros of 2x^2(x-1)=2 are x\approx 1.46557…

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

x \approx 1.46557 \dots

Solution steps

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

Expand

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

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

Move

2

to the left side

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

Find one solution for

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

using Newton-Raphson:

x \approx 1.46557 \dots

Apply long division:

\frac{2 x ^{3} - 2 x ^{2} - 2}{x - 1.46557 \dots} = 2 x^{2} + 0.93114 \dots x + 1.36465 \dots

2 x^{2} + 0.93114 \dots x + 1.36465 \dots \approx 0

Find one solution for

2 x^{2} + 0.93114 \dots x + 1.36465 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 1.46557 \dots

4 x + 5 = x^{3} + 2 x^{2} - x + 3

t^{3} - 2 t^{2} - 123 t + 540 = 0

114 s^{5} = 1.34 \cdot 10 - 34

x^{3} + 3 x - 4 = 5

(x) = (x - 5) (x + 2) (x - 4)

What are the solutions to the equation 2x^2(x-1)=2 ?
The solutions to the equation 2x^2(x-1)=2 are x\approx 1.46557…
Find the zeros of 2x^2(x-1)=2
The zeros of 2x^2(x-1)=2 are x\approx 1.46557…