Solve 2y^214y-240

Question

Simplify the expression

28 y^{3} - 240

Evaluate

2 y^{2} \times 14 y - 240

Solution

More Steps

Evaluate

2 y^{2} \times 14 y

Multiply the terms

28 y^{2} \times y

Multiply the terms with the same base by adding their exponents

28 y^{2 + 1}

Add the numbers

28 y^{3}

28 y^{3} - 240

Show Solution

Factor the expression

4 (7 y^{3} - 60)

Evaluate

2 y^{2} \times 14 y - 240

Multiply

More Steps

Evaluate

2 y^{2} \times 14 y

Multiply the terms

28 y^{2} \times y

Multiply the terms with the same base by adding their exponents

28 y^{2 + 1}

Add the numbers

28 y^{3}

28 y^{3} - 240

Solution

4 (7 y^{3} - 60)

Show Solution

Find the roots

y = \frac{3 2940}{7}

Alternative Form

y \approx 2.046528

Evaluate

2 y^{2} \times 14 y - 240

To find the roots of the expression,set the expression equal to 0

2 y^{2} \times 14 y - 240 = 0

Multiply

More Steps

Multiply the terms

2 y^{2} \times 14 y

Multiply the terms

28 y^{2} \times y

Multiply the terms with the same base by adding their exponents

28 y^{2 + 1}

Add the numbers

28 y^{3}

28 y^{3} - 240 = 0

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

28 y^{3} = 0 + 240

Removing 0 doesn't change the value,so remove it from the expression

28 y^{3} = 240

Divide both sides

\frac{28 y ^{3}}{28} = \frac{240}{28}

Divide the numbers

y^{3} = \frac{240}{28}

Cancel out the common factor 4

y^{3} = \frac{60}{7}

Take the 3 -th root on both sides of the equation

3 y^{3} = 3 \frac{60}{7}

Calculate

y = 3 \frac{60}{7}

Solution

More Steps

Evaluate

3 \frac{60}{7}

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

\frac{3 60}{3 7}

Multiply by the Conjugate

\frac{3 60 \times 3 7 ^{2}}{3 7 \times 3 7 ^{2}}

Simplify

\frac{3 60 \times 3 49}{3 7 \times 3 7 ^{2}}

Multiply the numbers

More Steps

Evaluate

360 \times 349

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

3 60 \times 49

Calculate the product

32940

\frac{3 2940}{3 7 \times 3 7 ^{2}}

Multiply the numbers

More Steps

Evaluate

37 \times 3 7^{2}

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

3 7 \times 7^{2}

Calculate the product

3 7^{3}

Reduce the index of the radical and exponent with 3

7

\frac{3 2940}{7}

y = \frac{3 2940}{7}

Alternative Form

y \approx 2.046528

Show Solution