Solve n^2 9n-3300=0

Question

Solve the equation

n = \frac{3 9900}{3}

Alternative Form

n \approx 7.157431

Evaluate

n^{2} \times 9 n - 3300 = 0

Multiply

More Steps

Evaluate

n^{2} \times 9 n

Multiply the terms with the same base by adding their exponents

n^{2 + 1} \times 9

Add the numbers

n^{3} \times 9

Use the commutative property to reorder the terms

9 n^{3}

9 n^{3} - 3300 = 0

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

9 n^{3} = 0 + 3300

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

9 n^{3} = 3300

Divide both sides

\frac{9 n ^{3}}{9} = \frac{3300}{9}

Divide the numbers

n^{3} = \frac{3300}{9}

Cancel out the common factor 3

n^{3} = \frac{1100}{3}

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

3 n^{3} = 3 \frac{1100}{3}

Calculate

n = 3 \frac{1100}{3}

Solution

More Steps

Evaluate

3 \frac{1100}{3}

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

\frac{3 1100}{3 3}

Multiply by the Conjugate

\frac{3 1100 \times 3 3 ^{2}}{3 3 \times 3 3 ^{2}}

Simplify

\frac{3 1100 \times 3 9}{3 3 \times 3 3 ^{2}}

Multiply the numbers

More Steps

Evaluate

31100 \times 39

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

3 1100 \times 9

Calculate the product

39900

\frac{3 9900}{3 3 \times 3 3 ^{2}}

Multiply the numbers

More Steps

Evaluate

33 \times 3 3^{2}

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

3 3 \times 3^{2}

Calculate the product

3 3^{3}

Reduce the index of the radical and exponent with 3

3

\frac{3 9900}{3}

n = \frac{3 9900}{3}

Alternative Form

n \approx 7.157431

Show Solution