Solve 5y^3y-16=180

Question

Solve the equation

y_{1} = - \frac{4 24500}{5}, y_{2} = \frac{4 24500}{5}

Alternative Form

y_{1} \approx - 2.502197, y_{2} \approx 2.502197

Evaluate

5 y^{3} \times y - 16 = 180

Multiply

More Steps

Evaluate

5 y^{3} \times y

Multiply the terms with the same base by adding their exponents

5 y^{3 + 1}

Add the numbers

5 y^{4}

5 y^{4} - 16 = 180

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

5 y^{4} = 180 + 16

Add the numbers

5 y^{4} = 196

Divide both sides

\frac{5 y ^{4}}{5} = \frac{196}{5}

Divide the numbers

y^{4} = \frac{196}{5}

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

y = \pm 4 \frac{196}{5}

Simplify the expression

More Steps

Evaluate

4 \frac{196}{5}

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

\frac{4 196}{4 5}

Simplify the radical expression

\frac{14}{4 5}

Multiply by the Conjugate

\frac{14 \times 4 5 ^{3}}{4 5 \times 4 5 ^{3}}

Simplify

\frac{14 \times 4 125}{4 5 \times 4 5 ^{3}}

Multiply the numbers

More Steps

Evaluate

14 \times 4125

Use n a = mn a^{m} to expand the expression

4 1 4^{2} \times 4125

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

4 1 4^{2} \times 125

Calculate the product

424500

\frac{4 24500}{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 24500}{5}

y = \pm \frac{4 24500}{5}

Separate the equation into 2 possible cases

y = \frac{4 24500}{5} y = - \frac{4 24500}{5}

Solution

y_{1} = - \frac{4 24500}{5}, y_{2} = \frac{4 24500}{5}

Alternative Form

y_{1} \approx - 2.502197, y_{2} \approx 2.502197

Show Solution