Solve 6x^2 33x - 18

Question

Simplify the expression

198 x^{3} - 18

Evaluate

6 x^{2} \times 33 x - 18

Solution

More Steps

Evaluate

6 x^{2} \times 33 x

Multiply the terms

198 x^{2} \times x

Multiply the terms with the same base by adding their exponents

198 x^{2 + 1}

Add the numbers

198 x^{3}

198 x^{3} - 18

Show Solution

Factor the expression

18 (11 x^{3} - 1)

Evaluate

6 x^{2} \times 33 x - 18

Multiply

More Steps

Evaluate

6 x^{2} \times 33 x

Multiply the terms

198 x^{2} \times x

Multiply the terms with the same base by adding their exponents

198 x^{2 + 1}

Add the numbers

198 x^{3}

198 x^{3} - 18

Solution

18 (11 x^{3} - 1)

Show Solution

Find the roots

x = \frac{3 121}{11}

Alternative Form

x \approx 0.449644

Evaluate

6 x^{2} \times 33 x - 18

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

6 x^{2} \times 33 x - 18 = 0

Multiply

More Steps

Multiply the terms

6 x^{2} \times 33 x

Multiply the terms

198 x^{2} \times x

Multiply the terms with the same base by adding their exponents

198 x^{2 + 1}

Add the numbers

198 x^{3}

198 x^{3} - 18 = 0

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

198 x^{3} = 0 + 18

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

198 x^{3} = 18

Divide both sides

\frac{198 x ^{3}}{198} = \frac{18}{198}

Divide the numbers

x^{3} = \frac{18}{198}

Cancel out the common factor 18

x^{3} = \frac{1}{11}

Take the 3 -th root on both sides of the equation

3 x^{3} = 3 \frac{1}{11}

Calculate

x = 3 \frac{1}{11}

Solution

More Steps

Evaluate

3 \frac{1}{11}

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

\frac{3 1}{3 11}

Simplify the radical expression

\frac{1}{3 11}

Multiply by the Conjugate

\frac{3 1 1 ^{2}}{3 11 \times 3 1 1 ^{2}}

Simplify

\frac{3 121}{3 11 \times 3 1 1 ^{2}}

Multiply the numbers

More Steps

Evaluate

311 \times 3 1 1^{2}

The product of roots with the same index is equal to the root of the product

3 11 \times 1 1^{2}

Calculate the product

3 1 1^{3}

Reduce the index of the radical and exponent with 3

11

\frac{3 121}{11}

x = \frac{3 121}{11}

Alternative Form

x \approx 0.449644

Show Solution