Solve 6x^224x-18x

Question

Simplify the expression

144 x^{3} - 18 x

Evaluate

6 x^{2} \times 24 x - 18 x

Solution

More Steps

Evaluate

6 x^{2} \times 24 x

Multiply the terms

144 x^{2} \times x

Multiply the terms with the same base by adding their exponents

144 x^{2 + 1}

Add the numbers

144 x^{3}

144 x^{3} - 18 x

Show Solution

Factor the expression

18 x (8 x^{2} - 1)

Evaluate

6 x^{2} \times 24 x - 18 x

Multiply

More Steps

Evaluate

6 x^{2} \times 24 x

Multiply the terms

144 x^{2} \times x

Multiply the terms with the same base by adding their exponents

144 x^{2 + 1}

Add the numbers

144 x^{3}

144 x^{3} - 18 x

Rewrite the expression

18 x \times 8 x^{2} - 18 x

Solution

18 x (8 x^{2} - 1)

Show Solution

Find the roots

x_{1} = - \frac{2}{4}, x_{2} = 0, x_{3} = \frac{2}{4}

Alternative Form

x_{1} \approx - 0.353553, x_{2} = 0, x_{3} \approx 0.353553

Evaluate

6 x^{2} \times 24 x - 18 x

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

6 x^{2} \times 24 x - 18 x = 0

Multiply

More Steps

Multiply the terms

6 x^{2} \times 24 x

Multiply the terms

144 x^{2} \times x

Multiply the terms with the same base by adding their exponents

144 x^{2 + 1}

Add the numbers

144 x^{3}

144 x^{3} - 18 x = 0

Factor the expression

18 x (8 x^{2} - 1) = 0

Divide both sides

x (8 x^{2} - 1) = 0

Separate the equation into 2 possible cases

x = 0 8 x^{2} - 1 = 0

Solve the equation

More Steps

Evaluate

8 x^{2} - 1 = 0

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

8 x^{2} = 0 + 1

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

8 x^{2} = 1

Divide both sides

\frac{8 x ^{2}}{8} = \frac{1}{8}

Divide the numbers

x^{2} = \frac{1}{8}

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

x = \pm \frac{1}{8}

Simplify the expression

More Steps

Evaluate

\frac{1}{8}

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

\frac{1}{8}

Simplify the radical expression

\frac{1}{8}

Simplify the radical expression

\frac{1}{2 2}

Multiply by the Conjugate

\frac{2}{2 2 \times 2}

Multiply the numbers

\frac{2}{4}

x = \pm \frac{2}{4}

Separate the equation into 2 possible cases

x = \frac{2}{4} x = - \frac{2}{4}

x = 0 x = \frac{2}{4} x = - \frac{2}{4}

Solution

x_{1} = - \frac{2}{4}, x_{2} = 0, x_{3} = \frac{2}{4}

Alternative Form

x_{1} \approx - 0.353553, x_{2} = 0, x_{3} \approx 0.353553

Show Solution