Solve -42x^4x-2 - ScanMath

Question

Simplify the expression

- 42 x^{5} - 2

Evaluate

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

Solution

More Steps

Evaluate

- 42 x^{4} \times x

Multiply the terms with the same base by adding their exponents

- 42 x^{4 + 1}

Add the numbers

- 42 x^{5}

- 42 x^{5} - 2

Show Solution

Factor the expression

- 2 (21 x^{5} + 1)

Evaluate

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

Multiply

More Steps

Evaluate

- 42 x^{4} \times x

Multiply the terms with the same base by adding their exponents

- 42 x^{4 + 1}

Add the numbers

- 42 x^{5}

- 42 x^{5} - 2

Solution

- 2 (21 x^{5} + 1)

Show Solution

Find the roots

x = - \frac{5 2 1 ^{4}}{21}

Alternative Form

x \approx - 0.543946

Evaluate

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

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

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

Multiply

More Steps

Multiply the terms

- 42 x^{4} \times x

Multiply the terms with the same base by adding their exponents

- 42 x^{4 + 1}

Add the numbers

- 42 x^{5}

- 42 x^{5} - 2 = 0

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

- 42 x^{5} = 0 + 2

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

- 42 x^{5} = 2

Change the signs on both sides of the equation

42 x^{5} = - 2

Divide both sides

\frac{42 x ^{5}}{42} = \frac{- 2}{42}

Divide the numbers

x^{5} = \frac{- 2}{42}

Divide the numbers

More Steps

Evaluate

\frac{- 2}{42}

Cancel out the common factor 2

\frac{- 1}{21}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

- \frac{1}{21}

x^{5} = - \frac{1}{21}

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

5 x^{5} = 5 - \frac{1}{21}

Calculate

x = 5 - \frac{1}{21}

Solution

More Steps

Evaluate

5 - \frac{1}{21}

An odd root of a negative radicand is always a negative

- 5 \frac{1}{21}

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

- \frac{5 1}{5 21}

Simplify the radical expression

- \frac{1}{5 21}

Multiply by the Conjugate

\frac{- 5 2 1 ^{4}}{5 21 \times 5 2 1 ^{4}}

Multiply the numbers

More Steps

Evaluate

521 \times 5 2 1^{4}

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

5 21 \times 2 1^{4}

Calculate the product

5 2 1^{5}

Reduce the index of the radical and exponent with 5

21

\frac{- 5 2 1 ^{4}}{21}

Calculate

- \frac{5 2 1 ^{4}}{21}

x = - \frac{5 2 1 ^{4}}{21}

Alternative Form

x \approx - 0.543946

Show Solution