Solve 3x^2 8x-16 - ScanMath

Question

Simplify the expression

24 x^{3} - 16

Evaluate

3 x^{2} \times 8 x - 16

Solution

More Steps

Evaluate

3 x^{2} \times 8 x

Multiply the terms

24 x^{2} \times x

Multiply the terms with the same base by adding their exponents

24 x^{2 + 1}

Add the numbers

24 x^{3}

24 x^{3} - 16

Show Solution

Factor the expression

8 (3 x^{3} - 2)

Evaluate

3 x^{2} \times 8 x - 16

Multiply

More Steps

Evaluate

3 x^{2} \times 8 x

Multiply the terms

24 x^{2} \times x

Multiply the terms with the same base by adding their exponents

24 x^{2 + 1}

Add the numbers

24 x^{3}

24 x^{3} - 16

Solution

8 (3 x^{3} - 2)

Show Solution

Find the roots

x = \frac{3 18}{3}

Alternative Form

x \approx 0.87358

Evaluate

3 x^{2} \times 8 x - 16

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

3 x^{2} \times 8 x - 16 = 0

Multiply

More Steps

Multiply the terms

3 x^{2} \times 8 x

Multiply the terms

24 x^{2} \times x

Multiply the terms with the same base by adding their exponents

24 x^{2 + 1}

Add the numbers

24 x^{3}

24 x^{3} - 16 = 0

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

24 x^{3} = 0 + 16

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

24 x^{3} = 16

Divide both sides

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

Divide the numbers

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

Cancel out the common factor 8

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

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

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

Calculate

x = 3 \frac{2}{3}

Solution

More Steps

Evaluate

3 \frac{2}{3}

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

\frac{3 2}{3 3}

Multiply by the Conjugate

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

Simplify

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

Multiply the numbers

More Steps

Evaluate

32 \times 39

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

3 2 \times 9

Calculate the product

318

\frac{3 18}{3 3 \times 3 3 ^{2}}

Multiply the numbers

More Steps

Evaluate

33 \times 3 3^{2}

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

3 3 \times 3^{2}

Calculate the product

3 3^{3}

Reduce the index of the radical and exponent with 3

3

\frac{3 18}{3}

x = \frac{3 18}{3}

Alternative Form

x \approx 0.87358

Show Solution