Solve -2(w^3) 7w=-31

Question

Solve the equation

w_{1} = - \frac{4 85064}{14}, w_{2} = \frac{4 85064}{14}

Alternative Form

w_{1} \approx - 1.219856, w_{2} \approx 1.219856

Evaluate

- 2 w^{3} \times 7 w = - 31

Multiply

More Steps

Evaluate

- 2 w^{3} \times 7 w

Multiply the terms

- 14 w^{3} \times w

Multiply the terms with the same base by adding their exponents

- 14 w^{3 + 1}

Add the numbers

- 14 w^{4}

- 14 w^{4} = - 31

Change the signs on both sides of the equation

14 w^{4} = 31

Divide both sides

\frac{14 w ^{4}}{14} = \frac{31}{14}

Divide the numbers

w^{4} = \frac{31}{14}

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

w = \pm 4 \frac{31}{14}

Simplify the expression

More Steps

Evaluate

4 \frac{31}{14}

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

\frac{4 31}{4 14}

Multiply by the Conjugate

\frac{4 31 \times 4 1 4 ^{3}}{4 14 \times 4 1 4 ^{3}}

Simplify

\frac{4 31 \times 4 2744}{4 14 \times 4 1 4 ^{3}}

Multiply the numbers

More Steps

Evaluate

431 \times 42744

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

4 31 \times 2744

Calculate the product

485064

\frac{4 85064}{4 14 \times 4 1 4 ^{3}}

Multiply the numbers

More Steps

Evaluate

414 \times 4 1 4^{3}

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

4 14 \times 1 4^{3}

Calculate the product

4 1 4^{4}

Reduce the index of the radical and exponent with 4

14

\frac{4 85064}{14}

w = \pm \frac{4 85064}{14}

Separate the equation into 2 possible cases

w = \frac{4 85064}{14} w = - \frac{4 85064}{14}

Solution

w_{1} = - \frac{4 85064}{14}, w_{2} = \frac{4 85064}{14}

Alternative Form

w_{1} \approx - 1.219856, w_{2} \approx 1.219856

Show Solution