Solve -7u^3u=-5-19

Question

Solve the equation

u_{1} = - \frac{4 8232}{7}, u_{2} = \frac{4 8232}{7}

Alternative Form

u_{1} \approx - 1.36075, u_{2} \approx 1.36075

Evaluate

- 7 u^{3} \times u = - 5 - 19

Multiply

More Steps

Evaluate

- 7 u^{3} \times u

Multiply the terms with the same base by adding their exponents

- 7 u^{3 + 1}

Add the numbers

- 7 u^{4}

- 7 u^{4} = - 5 - 19

Subtract the numbers

- 7 u^{4} = - 24

Change the signs on both sides of the equation

7 u^{4} = 24

Divide both sides

\frac{7 u ^{4}}{7} = \frac{24}{7}

Divide the numbers

u^{4} = \frac{24}{7}

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

u = \pm 4 \frac{24}{7}

Simplify the expression

More Steps

Evaluate

4 \frac{24}{7}

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

\frac{4 24}{4 7}

Multiply by the Conjugate

\frac{4 24 \times 4 7 ^{3}}{4 7 \times 4 7 ^{3}}

Simplify

\frac{4 24 \times 4 343}{4 7 \times 4 7 ^{3}}

Multiply the numbers

More Steps

Evaluate

424 \times 4343

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

4 24 \times 343

Calculate the product

48232

\frac{4 8232}{4 7 \times 4 7 ^{3}}

Multiply the numbers

More Steps

Evaluate

47 \times 4 7^{3}

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

4 7 \times 7^{3}

Calculate the product

4 7^{4}

Reduce the index of the radical and exponent with 4

7

\frac{4 8232}{7}

u = \pm \frac{4 8232}{7}

Separate the equation into 2 possible cases

u = \frac{4 8232}{7} u = - \frac{4 8232}{7}

Solution

u_{1} = - \frac{4 8232}{7}, u_{2} = \frac{4 8232}{7}

Alternative Form

u_{1} \approx - 1.36075, u_{2} \approx 1.36075

Show Solution