Solve 11x^2 110x=13200

Question

Solve the equation

x = \frac{2 3 1815}{11}

Alternative Form

x \approx 2.217836

Evaluate

11 x^{2} \times 110 x = 13200

Multiply

More Steps

Evaluate

11 x^{2} \times 110 x

Multiply the terms

1210 x^{2} \times x

Multiply the terms with the same base by adding their exponents

1210 x^{2 + 1}

Add the numbers

1210 x^{3}

1210 x^{3} = 13200

Divide both sides

\frac{1210 x ^{3}}{1210} = \frac{13200}{1210}

Divide the numbers

x^{3} = \frac{13200}{1210}

Cancel out the common factor 110

x^{3} = \frac{120}{11}

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

3 x^{3} = 3 \frac{120}{11}

Calculate

x = 3 \frac{120}{11}

Solution

More Steps

Evaluate

3 \frac{120}{11}

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

\frac{3 120}{3 11}

Simplify the radical expression

More Steps

Evaluate

3120

Write the expression as a product where the root of one of the factors can be evaluated

3 8 \times 15

Write the number in exponential form with the base of 2

3 2^{3} \times 15

The root of a product is equal to the product of the roots of each factor

3 2^{3} \times 315

Reduce the index of the radical and exponent with 3

2315

\frac{2 3 15}{3 11}

Multiply by the Conjugate

\frac{2 3 15 \times 3 1 1 ^{2}}{3 11 \times 3 1 1 ^{2}}

Simplify

\frac{2 3 15 \times 3 121}{3 11 \times 3 1 1 ^{2}}

Multiply the numbers

More Steps

Evaluate

315 \times 3121

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

3 15 \times 121

Calculate the product

31815

\frac{2 3 1815}{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{2 3 1815}{11}

x = \frac{2 3 1815}{11}

Alternative Form

x \approx 2.217836

Show Solution