Solve 36x^2 48x - 60

Question

Simplify the expression

1728 x^{3} - 60

Evaluate

36 x^{2} \times 48 x - 60

Solution

More Steps

Evaluate

36 x^{2} \times 48 x

Multiply the terms

1728 x^{2} \times x

Multiply the terms with the same base by adding their exponents

1728 x^{2 + 1}

Add the numbers

1728 x^{3}

1728 x^{3} - 60

Show Solution

Factor the expression

12 (144 x^{3} - 5)

Evaluate

36 x^{2} \times 48 x - 60

Multiply

More Steps

Evaluate

36 x^{2} \times 48 x

Multiply the terms

1728 x^{2} \times x

Multiply the terms with the same base by adding their exponents

1728 x^{2 + 1}

Add the numbers

1728 x^{3}

1728 x^{3} - 60

Solution

12 (144 x^{3} - 5)

Show Solution

Find the roots

x = \frac{3 60}{12}

Alternative Form

x \approx 0.326239

Evaluate

36 x^{2} \times 48 x - 60

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

36 x^{2} \times 48 x - 60 = 0

Multiply

More Steps

Multiply the terms

36 x^{2} \times 48 x

Multiply the terms

1728 x^{2} \times x

Multiply the terms with the same base by adding their exponents

1728 x^{2 + 1}

Add the numbers

1728 x^{3}

1728 x^{3} - 60 = 0

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

1728 x^{3} = 0 + 60

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

1728 x^{3} = 60

Divide both sides

\frac{1728 x ^{3}}{1728} = \frac{60}{1728}

Divide the numbers

x^{3} = \frac{60}{1728}

Cancel out the common factor 12

x^{3} = \frac{5}{144}

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

3 x^{3} = 3 \frac{5}{144}

Calculate

x = 3 \frac{5}{144}

Solution

More Steps

Evaluate

3 \frac{5}{144}

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

\frac{3 5}{3 144}

Simplify the radical expression

More Steps

Evaluate

3144

Write the expression as a product where the root of one of the factors can be evaluated

3 8 \times 18

Write the number in exponential form with the base of 2

3 2^{3} \times 18

The root of a product is equal to the product of the roots of each factor

3 2^{3} \times 318

Reduce the index of the radical and exponent with 3

2318

\frac{3 5}{2 3 18}

Multiply by the Conjugate

\frac{3 5 \times 3 1 8 ^{2}}{2 3 18 \times 3 1 8 ^{2}}

Simplify

\frac{3 5 \times 3 3 12}{2 3 18 \times 3 1 8 ^{2}}

Multiply the numbers

More Steps

Evaluate

35 \times 3312

Multiply the terms

360 \times 3

Use the commutative property to reorder the terms

3360

\frac{3 3 60}{2 3 18 \times 3 1 8 ^{2}}

Multiply the numbers

More Steps

Evaluate

2318 \times 3 1 8^{2}

Multiply the terms

2 \times 18

Multiply the terms

36

\frac{3 3 60}{36}

Cancel out the common factor 3

\frac{3 60}{12}

x = \frac{3 60}{12}

Alternative Form

x \approx 0.326239

Show Solution