Solve 2x^3-x - ScanMath

Question

Factor the expression

x (2 x^{2} - 1)

Evaluate

2 x^{3} - x

Rewrite the expression

x \times 2 x^{2} - x

Solution

x (2 x^{2} - 1)

Show Solution

x_{1} = - \frac{2}{2}, x_{2} = 0, x_{3} = \frac{2}{2}

Alternative Form

x_{1} \approx - 0.707107, x_{2} = 0, x_{3} \approx 0.707107

Evaluate

2 x^{3} - x

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

2 x^{3} - x = 0

Factor the expression

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

Separate the equation into 2 possible cases

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

Solve the equation

More Steps

Evaluate

2 x^{2} - 1 = 0

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

2 x^{2} = 0 + 1

Removing 0 doesn't change the value,so remove it from the expression

2 x^{2} = 1

Divide both sides

\frac{2 x ^{2}}{2} = \frac{1}{2}

Divide the numbers

x^{2} = \frac{1}{2}

Take the root of both sides of the equation and remember to use both positive and negative roots

x = \pm \frac{1}{2}

Simplify the expression

More Steps

Evaluate

\frac{1}{2}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{1}{2}

Simplify the radical expression

\frac{1}{2}

Multiply by the Conjugate

\frac{2}{2 \times 2}

When a square root of an expression is multiplied by itself,the result is that expression

\frac{2}{2}

x = \pm \frac{2}{2}

Separate the equation into 2 possible cases

x = \frac{2}{2} x = - \frac{2}{2}

x = 0 x = \frac{2}{2} x = - \frac{2}{2}

Solution

x_{1} = - \frac{2}{2}, x_{2} = 0, x_{3} = \frac{2}{2}

Alternative Form

x_{1} \approx - 0.707107, x_{2} = 0, x_{3} \approx 0.707107

Show Solution