Solve 5x^2 20x-60

Question

Simplify the expression

100 x^{3} - 60

Evaluate

5 x^{2} \times 20 x - 60

Solution

More Steps

Evaluate

5 x^{2} \times 20 x

Multiply the terms

100 x^{2} \times x

Multiply the terms with the same base by adding their exponents

100 x^{2 + 1}

Add the numbers

100 x^{3}

100 x^{3} - 60

Show Solution

Factor the expression

20 (5 x^{3} - 3)

Evaluate

5 x^{2} \times 20 x - 60

Multiply

More Steps

Evaluate

5 x^{2} \times 20 x

Multiply the terms

100 x^{2} \times x

Multiply the terms with the same base by adding their exponents

100 x^{2 + 1}

Add the numbers

100 x^{3}

100 x^{3} - 60

Solution

20 (5 x^{3} - 3)

Show Solution

Find the roots

x = \frac{3 75}{5}

Alternative Form

x \approx 0.843433

Evaluate

5 x^{2} \times 20 x - 60

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

5 x^{2} \times 20 x - 60 = 0

Multiply

More Steps

Multiply the terms

5 x^{2} \times 20 x

Multiply the terms

100 x^{2} \times x

Multiply the terms with the same base by adding their exponents

100 x^{2 + 1}

Add the numbers

100 x^{3}

100 x^{3} - 60 = 0

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

100 x^{3} = 0 + 60

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

100 x^{3} = 60

Divide both sides

\frac{100 x ^{3}}{100} = \frac{60}{100}

Divide the numbers

x^{3} = \frac{60}{100}

Cancel out the common factor 20

x^{3} = \frac{3}{5}

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

3 x^{3} = 3 \frac{3}{5}

Calculate

x = 3 \frac{3}{5}

Solution

More Steps

Evaluate

3 \frac{3}{5}

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

\frac{3 3}{3 5}

Multiply by the Conjugate

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

Simplify

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

Multiply the numbers

More Steps

Evaluate

33 \times 325

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

3 3 \times 25

Calculate the product

375

\frac{3 75}{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 75}{5}

x = \frac{3 75}{5}

Alternative Form

x \approx 0.843433

Show Solution