Solve 5x^3 x -21 = 7

Question

Solve the equation

x_{1} = - \frac{4 3500}{5}, x_{2} = \frac{4 3500}{5}

Alternative Form

x_{1} \approx - 1.538321, x_{2} \approx 1.538321

Evaluate

5 x^{3} \times x - 21 = 7

Multiply

More Steps

Evaluate

5 x^{3} \times x

Multiply the terms with the same base by adding their exponents

5 x^{3 + 1}

Add the numbers

5 x^{4}

5 x^{4} - 21 = 7

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

5 x^{4} = 7 + 21

Add the numbers

5 x^{4} = 28

Divide both sides

\frac{5 x ^{4}}{5} = \frac{28}{5}

Divide the numbers

x^{4} = \frac{28}{5}

Take the root of both sides of the equation and remember to use both positive and negative roots

x = \pm 4 \frac{28}{5}

Simplify the expression

More Steps

Evaluate

4 \frac{28}{5}

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

\frac{4 28}{4 5}

Multiply by the Conjugate

\frac{4 28 \times 4 5 ^{3}}{4 5 \times 4 5 ^{3}}

Simplify

\frac{4 28 \times 4 125}{4 5 \times 4 5 ^{3}}

Multiply the numbers

More Steps

Evaluate

428 \times 4125

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

4 28 \times 125

Calculate the product

43500

\frac{4 3500}{4 5 \times 4 5 ^{3}}

Multiply the numbers

More Steps

Evaluate

45 \times 4 5^{3}

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

4 5 \times 5^{3}

Calculate the product

4 5^{4}

Reduce the index of the radical and exponent with 4

5

\frac{4 3500}{5}

x = \pm \frac{4 3500}{5}

Separate the equation into 2 possible cases

x = \frac{4 3500}{5} x = - \frac{4 3500}{5}

Solution

x_{1} = - \frac{4 3500}{5}, x_{2} = \frac{4 3500}{5}

Alternative Form

x_{1} \approx - 1.538321, x_{2} \approx 1.538321

Show Solution