Solve 6x^(2) 12x-2

Question

Simplify the expression

72 x^{3} - 2

Evaluate

6 x^{2} \times 12 x - 2

Solution

More Steps

Evaluate

6 x^{2} \times 12 x

Multiply the terms

72 x^{2} \times x

Multiply the terms with the same base by adding their exponents

72 x^{2 + 1}

Add the numbers

72 x^{3}

72 x^{3} - 2

Show Solution

Factor the expression

2 (36 x^{3} - 1)

Evaluate

6 x^{2} \times 12 x - 2

Multiply

More Steps

Evaluate

6 x^{2} \times 12 x

Multiply the terms

72 x^{2} \times x

Multiply the terms with the same base by adding their exponents

72 x^{2 + 1}

Add the numbers

72 x^{3}

72 x^{3} - 2

Solution

2 (36 x^{3} - 1)

Show Solution

Find the roots

x = \frac{3 6}{6}

Alternative Form

x \approx 0.302853

Evaluate

6 x^{2} \times 12 x - 2

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

6 x^{2} \times 12 x - 2 = 0

Multiply

More Steps

Multiply the terms

6 x^{2} \times 12 x

Multiply the terms

72 x^{2} \times x

Multiply the terms with the same base by adding their exponents

72 x^{2 + 1}

Add the numbers

72 x^{3}

72 x^{3} - 2 = 0

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

72 x^{3} = 0 + 2

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

72 x^{3} = 2

Divide both sides

\frac{72 x ^{3}}{72} = \frac{2}{72}

Divide the numbers

x^{3} = \frac{2}{72}

Cancel out the common factor 2

x^{3} = \frac{1}{36}

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

3 x^{3} = 3 \frac{1}{36}

Calculate

x = 3 \frac{1}{36}

Solution

More Steps

Evaluate

3 \frac{1}{36}

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

\frac{3 1}{3 36}

Simplify the radical expression

\frac{1}{3 36}

Multiply by the Conjugate

\frac{3 3 6 ^{2}}{3 36 \times 3 3 6 ^{2}}

Simplify

\frac{6 3 6}{3 36 \times 3 3 6 ^{2}}

Multiply the numbers

More Steps

Evaluate

336 \times 3 3 6^{2}

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

3 36 \times 3 6^{2}

Calculate the product

3 3 6^{3}

Transform the expression

3 6^{6}

Reduce the index of the radical and exponent with 3

6^{2}

\frac{6 3 6}{6 ^{2}}

Reduce the fraction

More Steps

Evaluate

\frac{6}{6 ^{2}}

Use the product rule \frac{a ^{n}}{a ^{m}} = a^{n - m} to simplify the expression

\frac{1}{6 ^{2 - 1}}

Subtract the terms

\frac{1}{6 ^{1}}

Simplify

\frac{1}{6}

\frac{3 6}{6}

x = \frac{3 6}{6}

Alternative Form

x \approx 0.302853

Show Solution