Solve -2x^220x - 42

Question

Simplify the expression

- 40 x^{3} - 42

Evaluate

- 2 x^{2} \times 20 x - 42

Solution

More Steps

Evaluate

- 2 x^{2} \times 20 x

Multiply the terms

- 40 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 40 x^{2 + 1}

Add the numbers

- 40 x^{3}

- 40 x^{3} - 42

Show Solution

Factor the expression

- 2 (20 x^{3} + 21)

Evaluate

- 2 x^{2} \times 20 x - 42

Multiply

More Steps

Evaluate

- 2 x^{2} \times 20 x

Multiply the terms

- 40 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 40 x^{2 + 1}

Add the numbers

- 40 x^{3}

- 40 x^{3} - 42

Solution

- 2 (20 x^{3} + 21)

Show Solution

Find the roots

x = - \frac{3 1050}{10}

Alternative Form

x \approx - 1.016396

Evaluate

- 2 x^{2} \times 20 x - 42

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

- 2 x^{2} \times 20 x - 42 = 0

Multiply

More Steps

Multiply the terms

- 2 x^{2} \times 20 x

Multiply the terms

- 40 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 40 x^{2 + 1}

Add the numbers

- 40 x^{3}

- 40 x^{3} - 42 = 0

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

- 40 x^{3} = 0 + 42

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

- 40 x^{3} = 42

Change the signs on both sides of the equation

40 x^{3} = - 42

Divide both sides

\frac{40 x ^{3}}{40} = \frac{- 42}{40}

Divide the numbers

x^{3} = \frac{- 42}{40}

Divide the numbers

More Steps

Evaluate

\frac{- 42}{40}

Cancel out the common factor 2

\frac{- 21}{20}

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

- \frac{21}{20}

x^{3} = - \frac{21}{20}

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

3 x^{3} = 3 - \frac{21}{20}

Calculate

x = 3 - \frac{21}{20}

Solution

More Steps

Evaluate

3 - \frac{21}{20}

An odd root of a negative radicand is always a negative

- 3 \frac{21}{20}

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

- \frac{3 21}{3 20}

Multiply by the Conjugate

\frac{- 3 21 \times 3 2 0 ^{2}}{3 20 \times 3 2 0 ^{2}}

Simplify

\frac{- 3 21 \times 2 3 50}{3 20 \times 3 2 0 ^{2}}

Multiply the numbers

More Steps

Evaluate

- 321 \times 2350

Multiply the terms

- 31050 \times 2

Use the commutative property to reorder the terms

- 231050

\frac{- 2 3 1050}{3 20 \times 3 2 0 ^{2}}

Multiply the numbers

More Steps

Evaluate

320 \times 3 2 0^{2}

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

3 20 \times 2 0^{2}

Calculate the product

3 2 0^{3}

Reduce the index of the radical and exponent with 3

20

\frac{- 2 3 1050}{20}

Cancel out the common factor 2

\frac{- 3 1050}{10}

Calculate

- \frac{3 1050}{10}

x = - \frac{3 1050}{10}

Alternative Form

x \approx - 1.016396

Show Solution