Solve 3x^{2} 10x-8

Question

Simplify the expression

30 x^{3} - 8

Evaluate

3 x^{2} \times 10 x - 8

Solution

More Steps

Evaluate

3 x^{2} \times 10 x

Multiply the terms

30 x^{2} \times x

Multiply the terms with the same base by adding their exponents

30 x^{2 + 1}

Add the numbers

30 x^{3}

30 x^{3} - 8

Show Solution

Factor the expression

2 (15 x^{3} - 4)

Evaluate

3 x^{2} \times 10 x - 8

Multiply

More Steps

Evaluate

3 x^{2} \times 10 x

Multiply the terms

30 x^{2} \times x

Multiply the terms with the same base by adding their exponents

30 x^{2 + 1}

Add the numbers

30 x^{3}

30 x^{3} - 8

Solution

2 (15 x^{3} - 4)

Show Solution

Find the roots

x = \frac{3 900}{15}

Alternative Form

x \approx 0.64366

Evaluate

3 x^{2} \times 10 x - 8

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

3 x^{2} \times 10 x - 8 = 0

Multiply

More Steps

Multiply the terms

3 x^{2} \times 10 x

Multiply the terms

30 x^{2} \times x

Multiply the terms with the same base by adding their exponents

30 x^{2 + 1}

Add the numbers

30 x^{3}

30 x^{3} - 8 = 0

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

30 x^{3} = 0 + 8

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

30 x^{3} = 8

Divide both sides

\frac{30 x ^{3}}{30} = \frac{8}{30}

Divide the numbers

x^{3} = \frac{8}{30}

Cancel out the common factor 2

x^{3} = \frac{4}{15}

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

3 x^{3} = 3 \frac{4}{15}

Calculate

x = 3 \frac{4}{15}

Solution

More Steps

Evaluate

3 \frac{4}{15}

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

\frac{3 4}{3 15}

Multiply by the Conjugate

\frac{3 4 \times 3 1 5 ^{2}}{3 15 \times 3 1 5 ^{2}}

Simplify

\frac{3 4 \times 3 225}{3 15 \times 3 1 5 ^{2}}

Multiply the numbers

More Steps

Evaluate

34 \times 3225

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

3 4 \times 225

Calculate the product

3900

\frac{3 900}{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{3 900}{15}

x = \frac{3 900}{15}

Alternative Form

x \approx 0.64366

Show Solution