Solve 18x^3 -2x - ScanMath

Question

Factor the expression

2 x (3 x - 1) (3 x + 1)

Evaluate

18 x^{3} - 2 x

Factor out 2 x from the expression

2 x (9 x^{2} - 1)

Solution

More Steps

Evaluate

9 x^{2} - 1

Rewrite the expression in exponential form

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

Use a^{2} - b^{2} = (a - b) (a + b) to factor the expression

(3 x - 1) (3 x + 1)

2 x (3 x - 1) (3 x + 1)

Show Solution

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

Alternative Form

x_{1} = - 0. \dot{3}, x_{2} = 0, x_{3} = 0. \dot{3}

Evaluate

18 x^{3} - 2 x

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

18 x^{3} - 2 x = 0

Factor the expression

2 x (9 x^{2} - 1) = 0

Divide both sides

x (9 x^{2} - 1) = 0

Separate the equation into 2 possible cases

x = 0 9 x^{2} - 1 = 0

Solve the equation

More Steps

Evaluate

9 x^{2} - 1 = 0

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

9 x^{2} = 0 + 1

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

9 x^{2} = 1

Divide both sides

\frac{9 x ^{2}}{9} = \frac{1}{9}

Divide the numbers

x^{2} = \frac{1}{9}

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

x = \pm \frac{1}{9}

Simplify the expression

More Steps

Evaluate

\frac{1}{9}

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

\frac{1}{9}

Simplify the radical expression

\frac{1}{9}

Simplify the radical expression

\frac{1}{3}

x = \pm \frac{1}{3}

Separate the equation into 2 possible cases

x = \frac{1}{3} x = - \frac{1}{3}

x = 0 x = \frac{1}{3} x = - \frac{1}{3}

Solution

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

Alternative Form

x_{1} = - 0. \dot{3}, x_{2} = 0, x_{3} = 0. \dot{3}

Show Solution