Solve 15x^(2) 8x-8

Question

Simplify the expression

120 x^{3} - 8

Evaluate

15 x^{2} \times 8 x - 8

Solution

More Steps

Evaluate

15 x^{2} \times 8 x

Multiply the terms

120 x^{2} \times x

Multiply the terms with the same base by adding their exponents

120 x^{2 + 1}

Add the numbers

120 x^{3}

120 x^{3} - 8

Show Solution

Factor the expression

8 (15 x^{3} - 1)

Evaluate

15 x^{2} \times 8 x - 8

Multiply

More Steps

Evaluate

15 x^{2} \times 8 x

Multiply the terms

120 x^{2} \times x

Multiply the terms with the same base by adding their exponents

120 x^{2 + 1}

Add the numbers

120 x^{3}

120 x^{3} - 8

Solution

8 (15 x^{3} - 1)

Show Solution

Find the roots

x = \frac{3 225}{15}

Alternative Form

x \approx 0.40548

Evaluate

15 x^{2} \times 8 x - 8

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

15 x^{2} \times 8 x - 8 = 0

Multiply

More Steps

Multiply the terms

15 x^{2} \times 8 x

Multiply the terms

120 x^{2} \times x

Multiply the terms with the same base by adding their exponents

120 x^{2 + 1}

Add the numbers

120 x^{3}

120 x^{3} - 8 = 0

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

120 x^{3} = 0 + 8

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

120 x^{3} = 8

Divide both sides

\frac{120 x ^{3}}{120} = \frac{8}{120}

Divide the numbers

x^{3} = \frac{8}{120}

Cancel out the common factor 8

x^{3} = \frac{1}{15}

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

3 x^{3} = 3 \frac{1}{15}

Calculate

x = 3 \frac{1}{15}

Solution

More Steps

Evaluate

3 \frac{1}{15}

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

\frac{3 1}{3 15}

Simplify the radical expression

\frac{1}{3 15}

Multiply by the Conjugate

\frac{3 1 5 ^{2}}{3 15 \times 3 1 5 ^{2}}

Simplify

\frac{3 225}{3 15 \times 3 1 5 ^{2}}

Multiply the numbers

More Steps

Evaluate

315 \times 3 1 5^{2}

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

3 15 \times 1 5^{2}

Calculate the product

3 1 5^{3}

Reduce the index of the radical and exponent with 3

15

\frac{3 225}{15}

x = \frac{3 225}{15}

Alternative Form

x \approx 0.40548

Show Solution