Solve 3x^32x-8 - ScanMath

Question

Simplify the expression

6 x^{4} - 8

Evaluate

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

Solution

More Steps

Evaluate

3 x^{3} \times 2 x

Multiply the terms

6 x^{3} \times x

Multiply the terms with the same base by adding their exponents

6 x^{3 + 1}

Add the numbers

6 x^{4}

6 x^{4} - 8

Show Solution

Factor the expression

2 (3 x^{4} - 4)

Evaluate

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

Multiply

More Steps

Evaluate

3 x^{3} \times 2 x

Multiply the terms

6 x^{3} \times x

Multiply the terms with the same base by adding their exponents

6 x^{3 + 1}

Add the numbers

6 x^{4}

6 x^{4} - 8

Solution

2 (3 x^{4} - 4)

Show Solution

Find the roots

x_{1} = - \frac{4 108}{3}, x_{2} = \frac{4 108}{3}

Alternative Form

x_{1} \approx - 1.07457, x_{2} \approx 1.07457

Evaluate

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

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

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

Multiply

More Steps

Multiply the terms

3 x^{3} \times 2 x

Multiply the terms

6 x^{3} \times x

Multiply the terms with the same base by adding their exponents

6 x^{3 + 1}

Add the numbers

6 x^{4}

6 x^{4} - 8 = 0

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

6 x^{4} = 0 + 8

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

6 x^{4} = 8

Divide both sides

\frac{6 x ^{4}}{6} = \frac{8}{6}

Divide the numbers

x^{4} = \frac{8}{6}

Cancel out the common factor 2

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

Take the root of both sides of the equation and remember to use both positive and negative roots

x = \pm 4 \frac{4}{3}

Simplify the expression

More Steps

Evaluate

4 \frac{4}{3}

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

\frac{4 4}{4 3}

Simplify the radical expression

More Steps

Evaluate

44

Write the number in exponential form with the base of 2

4 2^{2}

Reduce the index of the radical and exponent with 2

2

\frac{2}{4 3}

Multiply by the Conjugate

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

Simplify

\frac{2 \times 4 27}{4 3 \times 4 3 ^{3}}

Multiply the numbers

More Steps

Evaluate

2 \times 427

Use n a = mn a^{m} to expand the expression

4 2^{2} \times 427

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

4 2^{2} \times 27

Calculate the product

4108

\frac{4 108}{4 3 \times 4 3 ^{3}}

Multiply the numbers

More Steps

Evaluate

43 \times 4 3^{3}

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

4 3 \times 3^{3}

Calculate the product

4 3^{4}

Reduce the index of the radical and exponent with 4

3

\frac{4 108}{3}

x = \pm \frac{4 108}{3}

Separate the equation into 2 possible cases

x = \frac{4 108}{3} x = - \frac{4 108}{3}

Solution

x_{1} = - \frac{4 108}{3}, x_{2} = \frac{4 108}{3}

Alternative Form

x_{1} \approx - 1.07457, x_{2} \approx 1.07457

Show Solution