Solve root(2x^2-2x 1)-2x^3

Question

Simplify the expression

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

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2 x \times (x - 1 - x^{2} 2 x)

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x = 0

Evaluate

2 x^{2} - 2 x \times 1 - 2 x^{3}

To find the roots of the expression,set the expression equal to 0

2 x^{2} - 2 x \times 1 - 2 x^{3} = 0

Find the domain

More Steps

2 x^{2} - 2 x \times 1 - 2 x^{3} = 0, x \in (- \infty, 0] \cup [1, + \infty)

Calculate

2 x^{2} - 2 x \times 1 - 2 x^{3} = 0

Multiply the terms

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

Move the expression to the right-hand side and change its sign

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

Evaluate

2 x^{2} - 2 x = 2 x^{3}, 2 x^{3} \geq 0

Evaluate

More Steps

2 x^{2} - 2 x = 2 x^{3}, x \geq 0

Solve the equation for x

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x = 0 x = - 1, x \geq 0

Find the intersection

x = 0

Check if the solution is in the defined range

x = 0, x \in (- \infty, 0] \cup [1, + \infty)

Solution

x = 0

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