Solve n^251n-12132=0

Question

Solve the equation

n = \frac{3 1168716}{17}

Alternative Form

n \approx 6.196133

Evaluate

n^{2} \times 51 n - 12132 = 0

Multiply

More Steps

Evaluate

n^{2} \times 51 n

Multiply the terms with the same base by adding their exponents

n^{2 + 1} \times 51

Add the numbers

n^{3} \times 51

Use the commutative property to reorder the terms

51 n^{3}

51 n^{3} - 12132 = 0

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

51 n^{3} = 0 + 12132

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

51 n^{3} = 12132

Divide both sides

\frac{51 n ^{3}}{51} = \frac{12132}{51}

Divide the numbers

n^{3} = \frac{12132}{51}

Cancel out the common factor 3

n^{3} = \frac{4044}{17}

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

3 n^{3} = 3 \frac{4044}{17}

Calculate

n = 3 \frac{4044}{17}

Solution

More Steps

Evaluate

3 \frac{4044}{17}

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

\frac{3 4044}{3 17}

Multiply by the Conjugate

\frac{3 4044 \times 3 1 7 ^{2}}{3 17 \times 3 1 7 ^{2}}

Simplify

\frac{3 4044 \times 3 289}{3 17 \times 3 1 7 ^{2}}

Multiply the numbers

More Steps

Evaluate

34044 \times 3289

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

3 4044 \times 289

Calculate the product

31168716

\frac{3 1168716}{3 17 \times 3 1 7 ^{2}}

Multiply the numbers

More Steps

Evaluate

317 \times 3 1 7^{2}

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

3 17 \times 1 7^{2}

Calculate the product

3 1 7^{3}

Reduce the index of the radical and exponent with 3

17

\frac{3 1168716}{17}

n = \frac{3 1168716}{17}

Alternative Form

n \approx 6.196133

Show Solution