Solve 9x^212x - 24 = 0

Question

Solve the equation

x = \frac{3 6}{3}

Alternative Form

x \approx 0.605707

Evaluate

9 x^{2} \times 12 x - 24 = 0

Multiply

More Steps

Evaluate

9 x^{2} \times 12 x

Multiply the terms

108 x^{2} \times x

Multiply the terms with the same base by adding their exponents

108 x^{2 + 1}

Add the numbers

108 x^{3}

108 x^{3} - 24 = 0

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

108 x^{3} = 0 + 24

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

108 x^{3} = 24

Divide both sides

\frac{108 x ^{3}}{108} = \frac{24}{108}

Divide the numbers

x^{3} = \frac{24}{108}

Cancel out the common factor 12

x^{3} = \frac{2}{9}

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

3 x^{3} = 3 \frac{2}{9}

Calculate

x = 3 \frac{2}{9}

Solution

More Steps

Evaluate

3 \frac{2}{9}

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

\frac{3 2}{3 9}

Multiply by the Conjugate

\frac{3 2 \times 3 9 ^{2}}{3 9 \times 3 9 ^{2}}

Simplify

\frac{3 2 \times 3 3 3}{3 9 \times 3 9 ^{2}}

Multiply the numbers

More Steps

Evaluate

32 \times 333

Multiply the terms

36 \times 3

Use the commutative property to reorder the terms

336

\frac{3 3 6}{3 9 \times 3 9 ^{2}}

Multiply the numbers

More Steps

Evaluate

39 \times 3 9^{2}

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

3 9 \times 9^{2}

Calculate the product

3 9^{3}

Transform the expression

3 3^{6}

Reduce the index of the radical and exponent with 3

3^{2}

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

Reduce the fraction

More Steps

Evaluate

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

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

\frac{1}{3 ^{2 - 1}}

Subtract the terms

\frac{1}{3 ^{1}}

Simplify

\frac{1}{3}

\frac{3 6}{3}

x = \frac{3 6}{3}

Alternative Form

x \approx 0.605707

Show Solution