Solve 9x^212x -120

Question

Simplify the expression

108 x^{3} - 120

Evaluate

9 x^{2} \times 12 x - 120

Solution

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} - 120

Show Solution

Factor the expression

12 (9 x^{3} - 10)

Evaluate

9 x^{2} \times 12 x - 120

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} - 120

Solution

12 (9 x^{3} - 10)

Show Solution

Find the roots

x = \frac{3 30}{3}

Alternative Form

x \approx 1.035744

Evaluate

9 x^{2} \times 12 x - 120

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

9 x^{2} \times 12 x - 120 = 0

Multiply

More Steps

Multiply the terms

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} - 120 = 0

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

108 x^{3} = 0 + 120

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

108 x^{3} = 120

Divide both sides

\frac{108 x ^{3}}{108} = \frac{120}{108}

Divide the numbers

x^{3} = \frac{120}{108}

Cancel out the common factor 12

x^{3} = \frac{10}{9}

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

3 x^{3} = 3 \frac{10}{9}

Calculate

x = 3 \frac{10}{9}

Solution

More Steps

Evaluate

3 \frac{10}{9}

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

\frac{3 10}{3 9}

Multiply by the Conjugate

\frac{3 10 \times 3 9 ^{2}}{3 9 \times 3 9 ^{2}}

Simplify

\frac{3 10 \times 3 3 3}{3 9 \times 3 9 ^{2}}

Multiply the numbers

More Steps

Evaluate

310 \times 333

Multiply the terms

330 \times 3

Use the commutative property to reorder the terms

3330

\frac{3 3 30}{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 30}{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 30}{3}

x = \frac{3 30}{3}

Alternative Form

x \approx 1.035744

Show Solution