Solve 6x^2 42x-48

Question

Simplify the expression

252 x^{3} - 48

Evaluate

6 x^{2} \times 42 x - 48

Solution

More Steps

Evaluate

6 x^{2} \times 42 x

Multiply the terms

252 x^{2} \times x

Multiply the terms with the same base by adding their exponents

252 x^{2 + 1}

Add the numbers

252 x^{3}

252 x^{3} - 48

Show Solution

Factor the expression

12 (21 x^{3} - 4)

Evaluate

6 x^{2} \times 42 x - 48

Multiply

More Steps

Evaluate

6 x^{2} \times 42 x

Multiply the terms

252 x^{2} \times x

Multiply the terms with the same base by adding their exponents

252 x^{2 + 1}

Add the numbers

252 x^{3}

252 x^{3} - 48

Solution

12 (21 x^{3} - 4)

Show Solution

Find the roots

x = \frac{3 1764}{21}

Alternative Form

x \approx 0.57537

Evaluate

6 x^{2} \times 42 x - 48

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

6 x^{2} \times 42 x - 48 = 0

Multiply

More Steps

Multiply the terms

6 x^{2} \times 42 x

Multiply the terms

252 x^{2} \times x

Multiply the terms with the same base by adding their exponents

252 x^{2 + 1}

Add the numbers

252 x^{3}

252 x^{3} - 48 = 0

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

252 x^{3} = 0 + 48

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

252 x^{3} = 48

Divide both sides

\frac{252 x ^{3}}{252} = \frac{48}{252}

Divide the numbers

x^{3} = \frac{48}{252}

Cancel out the common factor 12

x^{3} = \frac{4}{21}

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

3 x^{3} = 3 \frac{4}{21}

Calculate

x = 3 \frac{4}{21}

Solution

More Steps

Evaluate

3 \frac{4}{21}

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

\frac{3 4}{3 21}

Multiply by the Conjugate

\frac{3 4 \times 3 2 1 ^{2}}{3 21 \times 3 2 1 ^{2}}

Simplify

\frac{3 4 \times 3 441}{3 21 \times 3 2 1 ^{2}}

Multiply the numbers

More Steps

Evaluate

34 \times 3441

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

3 4 \times 441

Calculate the product

31764

\frac{3 1764}{3 21 \times 3 2 1 ^{2}}

Multiply the numbers

More Steps

Evaluate

321 \times 3 2 1^{2}

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

3 21 \times 2 1^{2}

Calculate the product

3 2 1^{3}

Reduce the index of the radical and exponent with 3

21

\frac{3 1764}{21}

x = \frac{3 1764}{21}

Alternative Form

x \approx 0.57537

Show Solution