Solve 4x^24x - 24

Question

Simplify the expression

16 x^{3} - 24

Evaluate

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

Solution

More Steps

Evaluate

4 x^{2} \times 4 x

Multiply the terms

16 x^{2} \times x

Multiply the terms with the same base by adding their exponents

16 x^{2 + 1}

Add the numbers

16 x^{3}

16 x^{3} - 24

Show Solution

Factor the expression

8 (2 x^{3} - 3)

Evaluate

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

Multiply

More Steps

Evaluate

4 x^{2} \times 4 x

Multiply the terms

16 x^{2} \times x

Multiply the terms with the same base by adding their exponents

16 x^{2 + 1}

Add the numbers

16 x^{3}

16 x^{3} - 24

Solution

8 (2 x^{3} - 3)

Show Solution

Find the roots

x = \frac{3 12}{2}

Alternative Form

x \approx 1.144714

Evaluate

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

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

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

Multiply

More Steps

Multiply the terms

4 x^{2} \times 4 x

Multiply the terms

16 x^{2} \times x

Multiply the terms with the same base by adding their exponents

16 x^{2 + 1}

Add the numbers

16 x^{3}

16 x^{3} - 24 = 0

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

16 x^{3} = 0 + 24

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

16 x^{3} = 24

Divide both sides

\frac{16 x ^{3}}{16} = \frac{24}{16}

Divide the numbers

x^{3} = \frac{24}{16}

Cancel out the common factor 8

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

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

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

Calculate

x = 3 \frac{3}{2}

Solution

More Steps

Evaluate

3 \frac{3}{2}

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

\frac{3 3}{3 2}

Multiply by the Conjugate

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

Simplify

\frac{3 3 \times 3 4}{3 2 \times 3 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

33 \times 34

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

3 3 \times 4

Calculate the product

312

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

Multiply the numbers

More Steps

Evaluate

32 \times 3 2^{2}

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

3 2 \times 2^{2}

Calculate the product

3 2^{3}

Reduce the index of the radical and exponent with 3

2

\frac{3 12}{2}

x = \frac{3 12}{2}

Alternative Form

x \approx 1.144714

Show Solution