Solve n^2 21n - 270

Question

Simplify the expression

21 n^{3} - 270

Evaluate

n^{2} \times 21 n - 270

Solution

More Steps

Evaluate

n^{2} \times 21 n

Multiply the terms with the same base by adding their exponents

n^{2 + 1} \times 21

Add the numbers

n^{3} \times 21

Use the commutative property to reorder the terms

21 n^{3}

21 n^{3} - 270

Show Solution

Factor the expression

3 (7 n^{3} - 90)

Evaluate

n^{2} \times 21 n - 270

Multiply

More Steps

Evaluate

n^{2} \times 21 n

Multiply the terms with the same base by adding their exponents

n^{2 + 1} \times 21

Add the numbers

n^{3} \times 21

Use the commutative property to reorder the terms

21 n^{3}

21 n^{3} - 270

Solution

3 (7 n^{3} - 90)

Show Solution

Find the roots

n = \frac{3 4410}{7}

Alternative Form

n \approx 2.34269

Evaluate

n^{2} \times 21 n - 270

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

n^{2} \times 21 n - 270 = 0

Multiply

More Steps

Multiply the terms

n^{2} \times 21 n

Multiply the terms with the same base by adding their exponents

n^{2 + 1} \times 21

Add the numbers

n^{3} \times 21

Use the commutative property to reorder the terms

21 n^{3}

21 n^{3} - 270 = 0

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

21 n^{3} = 0 + 270

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

21 n^{3} = 270

Divide both sides

\frac{21 n ^{3}}{21} = \frac{270}{21}

Divide the numbers

n^{3} = \frac{270}{21}

Cancel out the common factor 3

n^{3} = \frac{90}{7}

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

3 n^{3} = 3 \frac{90}{7}

Calculate

n = 3 \frac{90}{7}

Solution

More Steps

Evaluate

3 \frac{90}{7}

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

\frac{3 90}{3 7}

Multiply by the Conjugate

\frac{3 90 \times 3 7 ^{2}}{3 7 \times 3 7 ^{2}}

Simplify

\frac{3 90 \times 3 49}{3 7 \times 3 7 ^{2}}

Multiply the numbers

More Steps

Evaluate

390 \times 349

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

3 90 \times 49

Calculate the product

34410

\frac{3 4410}{3 7 \times 3 7 ^{2}}

Multiply the numbers

More Steps

Evaluate

37 \times 3 7^{2}

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

3 7 \times 7^{2}

Calculate the product

3 7^{3}

Reduce the index of the radical and exponent with 3

7

\frac{3 4410}{7}

n = \frac{3 4410}{7}

Alternative Form

n \approx 2.34269

Show Solution