Solve 11x^2 33x-110

Question

Simplify the expression

363 x^{3} - 110

Evaluate

11 x^{2} \times 33 x - 110

Solution

More Steps

Evaluate

11 x^{2} \times 33 x

Multiply the terms

363 x^{2} \times x

Multiply the terms with the same base by adding their exponents

363 x^{2 + 1}

Add the numbers

363 x^{3}

363 x^{3} - 110

Show Solution

Factor the expression

11 (33 x^{3} - 10)

Evaluate

11 x^{2} \times 33 x - 110

Multiply

More Steps

Evaluate

11 x^{2} \times 33 x

Multiply the terms

363 x^{2} \times x

Multiply the terms with the same base by adding their exponents

363 x^{2 + 1}

Add the numbers

363 x^{3}

363 x^{3} - 110

Solution

11 (33 x^{3} - 10)

Show Solution

Find the roots

x = \frac{3 10890}{33}

Alternative Form

x \approx 0.671679

Evaluate

11 x^{2} \times 33 x - 110

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

11 x^{2} \times 33 x - 110 = 0

Multiply

More Steps

Multiply the terms

11 x^{2} \times 33 x

Multiply the terms

363 x^{2} \times x

Multiply the terms with the same base by adding their exponents

363 x^{2 + 1}

Add the numbers

363 x^{3}

363 x^{3} - 110 = 0

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

363 x^{3} = 0 + 110

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

363 x^{3} = 110

Divide both sides

\frac{363 x ^{3}}{363} = \frac{110}{363}

Divide the numbers

x^{3} = \frac{110}{363}

Cancel out the common factor 11

x^{3} = \frac{10}{33}

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

3 x^{3} = 3 \frac{10}{33}

Calculate

x = 3 \frac{10}{33}

Solution

More Steps

Evaluate

3 \frac{10}{33}

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

\frac{3 10}{3 33}

Multiply by the Conjugate

\frac{3 10 \times 3 3 3 ^{2}}{3 33 \times 3 3 3 ^{2}}

Simplify

\frac{3 10 \times 3 1089}{3 33 \times 3 3 3 ^{2}}

Multiply the numbers

More Steps

Evaluate

310 \times 31089

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

3 10 \times 1089

Calculate the product

310890

\frac{3 10890}{3 33 \times 3 3 3 ^{2}}

Multiply the numbers

More Steps

Evaluate

333 \times 3 3 3^{2}

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

3 33 \times 3 3^{2}

Calculate the product

3 3 3^{3}

Reduce the index of the radical and exponent with 3

33

\frac{3 10890}{33}

x = \frac{3 10890}{33}

Alternative Form

x \approx 0.671679

Show Solution