Solve 5s^2 10s-40

Question

Simplify the expression

50 s^{3} - 40

Evaluate

5 s^{2} \times 10 s - 40

Solution

More Steps

Evaluate

5 s^{2} \times 10 s

Multiply the terms

50 s^{2} \times s

Multiply the terms with the same base by adding their exponents

50 s^{2 + 1}

Add the numbers

50 s^{3}

50 s^{3} - 40

Show Solution

Factor the expression

10 (5 s^{3} - 4)

Evaluate

5 s^{2} \times 10 s - 40

Multiply

More Steps

Evaluate

5 s^{2} \times 10 s

Multiply the terms

50 s^{2} \times s

Multiply the terms with the same base by adding their exponents

50 s^{2 + 1}

Add the numbers

50 s^{3}

50 s^{3} - 40

Solution

10 (5 s^{3} - 4)

Show Solution

Find the roots

s = \frac{3 100}{5}

Alternative Form

s \approx 0.928318

Evaluate

5 s^{2} \times 10 s - 40

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

5 s^{2} \times 10 s - 40 = 0

Multiply

More Steps

Multiply the terms

5 s^{2} \times 10 s

Multiply the terms

50 s^{2} \times s

Multiply the terms with the same base by adding their exponents

50 s^{2 + 1}

Add the numbers

50 s^{3}

50 s^{3} - 40 = 0

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

50 s^{3} = 0 + 40

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

50 s^{3} = 40

Divide both sides

\frac{50 s ^{3}}{50} = \frac{40}{50}

Divide the numbers

s^{3} = \frac{40}{50}

Cancel out the common factor 10

s^{3} = \frac{4}{5}

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

3 s^{3} = 3 \frac{4}{5}

Calculate

s = 3 \frac{4}{5}

Solution

More Steps

Evaluate

3 \frac{4}{5}

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

\frac{3 4}{3 5}

Multiply by the Conjugate

\frac{3 4 \times 3 5 ^{2}}{3 5 \times 3 5 ^{2}}

Simplify

\frac{3 4 \times 3 25}{3 5 \times 3 5 ^{2}}

Multiply the numbers

More Steps

Evaluate

34 \times 325

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

3 4 \times 25

Calculate the product

3100

\frac{3 100}{3 5 \times 3 5 ^{2}}

Multiply the numbers

More Steps

Evaluate

35 \times 3 5^{2}

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

3 5 \times 5^{2}

Calculate the product

3 5^{3}

Reduce the index of the radical and exponent with 3

5

\frac{3 100}{5}

s = \frac{3 100}{5}

Alternative Form

s \approx 0.928318

Show Solution