Solve y^2 10y-1975

Question

Simplify the expression

10 y^{3} - 1975

Evaluate

y^{2} \times 10 y - 1975

Solution

More Steps

Evaluate

y^{2} \times 10 y

Multiply the terms with the same base by adding their exponents

y^{2 + 1} \times 10

Add the numbers

y^{3} \times 10

Use the commutative property to reorder the terms

10 y^{3}

10 y^{3} - 1975

Show Solution

Factor the expression

5 (2 y^{3} - 395)

Evaluate

y^{2} \times 10 y - 1975

Multiply

More Steps

Evaluate

y^{2} \times 10 y

Multiply the terms with the same base by adding their exponents

y^{2 + 1} \times 10

Add the numbers

y^{3} \times 10

Use the commutative property to reorder the terms

10 y^{3}

10 y^{3} - 1975

Solution

5 (2 y^{3} - 395)

Show Solution

Find the roots

y = \frac{3 1580}{2}

Alternative Form

y \approx 5.823566

Evaluate

y^{2} \times 10 y - 1975

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

y^{2} \times 10 y - 1975 = 0

Multiply

More Steps

Multiply the terms

y^{2} \times 10 y

Multiply the terms with the same base by adding their exponents

y^{2 + 1} \times 10

Add the numbers

y^{3} \times 10

Use the commutative property to reorder the terms

10 y^{3}

10 y^{3} - 1975 = 0

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

10 y^{3} = 0 + 1975

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

10 y^{3} = 1975

Divide both sides

\frac{10 y ^{3}}{10} = \frac{1975}{10}

Divide the numbers

y^{3} = \frac{1975}{10}

Cancel out the common factor 5

y^{3} = \frac{395}{2}

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

3 y^{3} = 3 \frac{395}{2}

Calculate

y = 3 \frac{395}{2}

Solution

More Steps

Evaluate

3 \frac{395}{2}

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

\frac{3 395}{3 2}

Multiply by the Conjugate

\frac{3 395 \times 3 2 ^{2}}{3 2 \times 3 2 ^{2}}

Simplify

\frac{3 395 \times 3 4}{3 2 \times 3 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

3395 \times 34

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

3 395 \times 4

Calculate the product

31580

\frac{3 1580}{3 2 \times 3 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

32 \times 3 2^{2}

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

3 2 \times 2^{2}

Calculate the product

3 2^{3}

Reduce the index of the radical and exponent with 3

2

\frac{3 1580}{2}

y = \frac{3 1580}{2}

Alternative Form

y \approx 5.823566

Show Solution