Solve 3x^4x-10=21

Question

Solve the equation

x = \frac{5 2511}{3}

Alternative Form

x \approx 1.595321

Evaluate

3 x^{4} \times x - 10 = 21

Multiply

More Steps

Evaluate

3 x^{4} \times x

Multiply the terms with the same base by adding their exponents

3 x^{4 + 1}

Add the numbers

3 x^{5}

3 x^{5} - 10 = 21

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

3 x^{5} = 21 + 10

Add the numbers

3 x^{5} = 31

Divide both sides

\frac{3 x ^{5}}{3} = \frac{31}{3}

Divide the numbers

x^{5} = \frac{31}{3}

Take the 5 -th root on both sides of the equation

5 x^{5} = 5 \frac{31}{3}

Calculate

x = 5 \frac{31}{3}

Solution

More Steps

Evaluate

5 \frac{31}{3}

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

\frac{5 31}{5 3}

Multiply by the Conjugate

\frac{5 31 \times 5 3 ^{4}}{5 3 \times 5 3 ^{4}}

Simplify

\frac{5 31 \times 5 81}{5 3 \times 5 3 ^{4}}

Multiply the numbers

More Steps

Evaluate

531 \times 581

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

5 31 \times 81

Calculate the product

52511

\frac{5 2511}{5 3 \times 5 3 ^{4}}

Multiply the numbers

More Steps

Evaluate

53 \times 5 3^{4}

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

5 3 \times 3^{4}

Calculate the product

5 3^{5}

Reduce the index of the radical and exponent with 5

3

\frac{5 2511}{3}

x = \frac{5 2511}{3}

Alternative Form

x \approx 1.595321

Show Solution