Solve 3x^212x - 15

Question

Simplify the expression

36 x^{3} - 15

Evaluate

3 x^{2} \times 12 x - 15

Solution

More Steps

Evaluate

3 x^{2} \times 12 x

Multiply the terms

36 x^{2} \times x

Multiply the terms with the same base by adding their exponents

36 x^{2 + 1}

Add the numbers

36 x^{3}

36 x^{3} - 15

Show Solution

Factor the expression

3 (12 x^{3} - 5)

Evaluate

3 x^{2} \times 12 x - 15

Multiply

More Steps

Evaluate

3 x^{2} \times 12 x

Multiply the terms

36 x^{2} \times x

Multiply the terms with the same base by adding their exponents

36 x^{2 + 1}

Add the numbers

36 x^{3}

36 x^{3} - 15

Solution

3 (12 x^{3} - 5)

Show Solution

Find the roots

x = \frac{3 90}{6}

Alternative Form

x \approx 0.746901

Evaluate

3 x^{2} \times 12 x - 15

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

3 x^{2} \times 12 x - 15 = 0

Multiply

More Steps

Multiply the terms

3 x^{2} \times 12 x

Multiply the terms

36 x^{2} \times x

Multiply the terms with the same base by adding their exponents

36 x^{2 + 1}

Add the numbers

36 x^{3}

36 x^{3} - 15 = 0

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

36 x^{3} = 0 + 15

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

36 x^{3} = 15

Divide both sides

\frac{36 x ^{3}}{36} = \frac{15}{36}

Divide the numbers

x^{3} = \frac{15}{36}

Cancel out the common factor 3

x^{3} = \frac{5}{12}

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

3 x^{3} = 3 \frac{5}{12}

Calculate

x = 3 \frac{5}{12}

Solution

More Steps

Evaluate

3 \frac{5}{12}

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

\frac{3 5}{3 12}

Multiply by the Conjugate

\frac{3 5 \times 3 1 2 ^{2}}{3 12 \times 3 1 2 ^{2}}

Simplify

\frac{3 5 \times 2 3 18}{3 12 \times 3 1 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

35 \times 2318

Multiply the terms

390 \times 2

Use the commutative property to reorder the terms

2390

\frac{2 3 90}{3 12 \times 3 1 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

312 \times 3 1 2^{2}

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

3 12 \times 1 2^{2}

Calculate the product

3 1 2^{3}

Reduce the index of the radical and exponent with 3

12

\frac{2 3 90}{12}

Cancel out the common factor 2

\frac{3 90}{6}

x = \frac{3 90}{6}

Alternative Form

x \approx 0.746901

Show Solution