Solve 6n^2 13n-603

Question

Simplify the expression

78 n^{3} - 603

Evaluate

6 n^{2} \times 13 n - 603

Solution

More Steps

Evaluate

6 n^{2} \times 13 n

Multiply the terms

78 n^{2} \times n

Multiply the terms with the same base by adding their exponents

78 n^{2 + 1}

Add the numbers

78 n^{3}

78 n^{3} - 603

Show Solution

Factor the expression

3 (26 n^{3} - 201)

Evaluate

6 n^{2} \times 13 n - 603

Multiply

More Steps

Evaluate

6 n^{2} \times 13 n

Multiply the terms

78 n^{2} \times n

Multiply the terms with the same base by adding their exponents

78 n^{2 + 1}

Add the numbers

78 n^{3}

78 n^{3} - 603

Solution

3 (26 n^{3} - 201)

Show Solution

Find the roots

n = \frac{3 135876}{26}

Alternative Form

n \approx 1.977308

Evaluate

6 n^{2} \times 13 n - 603

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

6 n^{2} \times 13 n - 603 = 0

Multiply

More Steps

Multiply the terms

6 n^{2} \times 13 n

Multiply the terms

78 n^{2} \times n

Multiply the terms with the same base by adding their exponents

78 n^{2 + 1}

Add the numbers

78 n^{3}

78 n^{3} - 603 = 0

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

78 n^{3} = 0 + 603

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

78 n^{3} = 603

Divide both sides

\frac{78 n ^{3}}{78} = \frac{603}{78}

Divide the numbers

n^{3} = \frac{603}{78}

Cancel out the common factor 3

n^{3} = \frac{201}{26}

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

3 n^{3} = 3 \frac{201}{26}

Calculate

n = 3 \frac{201}{26}

Solution

More Steps

Evaluate

3 \frac{201}{26}

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

\frac{3 201}{3 26}

Multiply by the Conjugate

\frac{3 201 \times 3 2 6 ^{2}}{3 26 \times 3 2 6 ^{2}}

Simplify

\frac{3 201 \times 3 676}{3 26 \times 3 2 6 ^{2}}

Multiply the numbers

More Steps

Evaluate

3201 \times 3676

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

3 201 \times 676

Calculate the product

3135876

\frac{3 135876}{3 26 \times 3 2 6 ^{2}}

Multiply the numbers

More Steps

Evaluate

326 \times 3 2 6^{2}

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

3 26 \times 2 6^{2}

Calculate the product

3 2 6^{3}

Reduce the index of the radical and exponent with 3

26

\frac{3 135876}{26}

n = \frac{3 135876}{26}

Alternative Form

n \approx 1.977308

Show Solution