Solve 3x^2 x - 1/12 = 0

Question

Solve the equation

x = \frac{3 6}{6}

Alternative Form

x \approx 0.302853

Evaluate

3 x^{2} \times x - \frac{1}{12} = 0

Multiply

More Steps

Evaluate

3 x^{2} \times x

Multiply the terms with the same base by adding their exponents

3 x^{2 + 1}

Add the numbers

3 x^{3}

3 x^{3} - \frac{1}{12} = 0

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

3 x^{3} = 0 + \frac{1}{12}

Add the terms

3 x^{3} = \frac{1}{12}

Multiply by the reciprocal

3 x^{3} \times \frac{1}{3} = \frac{1}{12} \times \frac{1}{3}

Multiply

x^{3} = \frac{1}{12} \times \frac{1}{3}

Multiply

More Steps

Evaluate

\frac{1}{12} \times \frac{1}{3}

To multiply the fractions,multiply the numerators and denominators separately

\frac{1}{12 \times 3}

Multiply the numbers

\frac{1}{36}

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