Solve 4x^42x -2 - ScanMath

Question

Simplify the expression

8 x^{5} - 2

Evaluate

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

Solution

More Steps

Evaluate

4 x^{4} \times 2 x

Multiply the terms

8 x^{4} \times x

Multiply the terms with the same base by adding their exponents

8 x^{4 + 1}

Add the numbers

8 x^{5}

8 x^{5} - 2

Show Solution

Factor the expression

2 (4 x^{5} - 1)

Evaluate

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

Multiply

More Steps

Evaluate

4 x^{4} \times 2 x

Multiply the terms

8 x^{4} \times x

Multiply the terms with the same base by adding their exponents

8 x^{4 + 1}

Add the numbers

8 x^{5}

8 x^{5} - 2

Solution

2 (4 x^{5} - 1)

Show Solution

Find the roots

x = \frac{5 8}{2}

Alternative Form

x \approx 0.757858

Evaluate

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

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

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

Multiply

More Steps

Multiply the terms

4 x^{4} \times 2 x

Multiply the terms

8 x^{4} \times x

Multiply the terms with the same base by adding their exponents

8 x^{4 + 1}

Add the numbers

8 x^{5}

8 x^{5} - 2 = 0

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

8 x^{5} = 0 + 2

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

8 x^{5} = 2

Divide both sides

\frac{8 x ^{5}}{8} = \frac{2}{8}

Divide the numbers

x^{5} = \frac{2}{8}

Cancel out the common factor 2

x^{5} = \frac{1}{4}

Take the 5 -th root on both sides of the equation

5 x^{5} = 5 \frac{1}{4}

Calculate

x = 5 \frac{1}{4}

Solution

More Steps

Evaluate

5 \frac{1}{4}

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

\frac{5 1}{5 4}

Simplify the radical expression

\frac{1}{5 4}

Multiply by the Conjugate

\frac{5 4 ^{4}}{5 4 \times 5 4 ^{4}}

Simplify

\frac{2 5 8}{5 4 \times 5 4 ^{4}}

Multiply the numbers

More Steps

Evaluate

54 \times 5 4^{4}

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

5 4 \times 4^{4}

Calculate the product

5 4^{5}

Transform the expression

5 2^{10}

Reduce the index of the radical and exponent with 5

2^{2}

\frac{2 5 8}{2 ^{2}}

Reduce the fraction

More Steps

Evaluate

\frac{2}{2 ^{2}}

Use the product rule \frac{a ^{n}}{a ^{m}} = a^{n - m} to simplify the expression

\frac{1}{2 ^{2 - 1}}

Subtract the terms

\frac{1}{2 ^{1}}

Simplify

\frac{1}{2}

\frac{5 8}{2}

x = \frac{5 8}{2}

Alternative Form

x \approx 0.757858

Show Solution