Solve 1/4x^2 x-24

Question

Simplify the expression

\frac{1}{4} x^{3} - 24

Evaluate

\frac{1}{4} x^{2} \times x - 24

Solution

More Steps

Evaluate

\frac{1}{4} x^{2} \times x

Multiply the terms with the same base by adding their exponents

\frac{1}{4} x^{2 + 1}

Add the numbers

\frac{1}{4} x^{3}

\frac{1}{4} x^{3} - 24

Show Solution

\frac{1}{4} (x^{3} - 96)

Evaluate

\frac{1}{4} x^{2} \times x - 24

Multiply

More Steps

Evaluate

\frac{1}{4} x^{2} \times x

Multiply the terms with the same base by adding their exponents

\frac{1}{4} x^{2 + 1}

Add the numbers

\frac{1}{4} x^{3}

\frac{1}{4} x^{3} - 24

Solution

\frac{1}{4} (x^{3} - 96)

Show Solution

x = 2312

Alternative Form

x \approx 4.578857

Evaluate

\frac{1}{4} x^{2} \times x - 24

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

\frac{1}{4} x^{2} \times x - 24 = 0

Multiply

More Steps

Multiply the terms

\frac{1}{4} x^{2} \times x

Multiply the terms with the same base by adding their exponents

\frac{1}{4} x^{2 + 1}

Add the numbers

\frac{1}{4} x^{3}

\frac{1}{4} x^{3} - 24 = 0

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

\frac{1}{4} x^{3} = 0 + 24

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

\frac{1}{4} x^{3} = 24

Multiply by the reciprocal

\frac{1}{4} x^{3} \times 4 = 24 \times 4

Multiply

x^{3} = 24 \times 4

Multiply

x^{3} = 96

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

3 x^{3} = 396

Calculate

x = 396

Solution

More Steps

Evaluate

396

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

3 8 \times 12

Write the number in exponential form with the base of 2

3 2^{3} \times 12

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

3 2^{3} \times 312

Reduce the index of the radical and exponent with 3

2312

x = 2312

Alternative Form

x \approx 4.578857

Show Solution