Solve -2x^222x-56

Question

Simplify the expression

- 44 x^{3} - 56

Evaluate

- 2 x^{2} \times 22 x - 56

Solution

More Steps

Evaluate

- 2 x^{2} \times 22 x

Multiply the terms

- 44 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 44 x^{2 + 1}

Add the numbers

- 44 x^{3}

- 44 x^{3} - 56

Show Solution

Factor the expression

- 4 (11 x^{3} + 14)

Evaluate

- 2 x^{2} \times 22 x - 56

Multiply

More Steps

Evaluate

- 2 x^{2} \times 22 x

Multiply the terms

- 44 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 44 x^{2 + 1}

Add the numbers

- 44 x^{3}

- 44 x^{3} - 56

Solution

- 4 (11 x^{3} + 14)

Show Solution

Find the roots

x = - \frac{3 1694}{11}

Alternative Form

x \approx - 1.083707

Evaluate

- 2 x^{2} \times 22 x - 56

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

- 2 x^{2} \times 22 x - 56 = 0

Multiply

More Steps

Multiply the terms

- 2 x^{2} \times 22 x

Multiply the terms

- 44 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 44 x^{2 + 1}

Add the numbers

- 44 x^{3}

- 44 x^{3} - 56 = 0

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

- 44 x^{3} = 0 + 56

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

- 44 x^{3} = 56

Change the signs on both sides of the equation

44 x^{3} = - 56

Divide both sides

\frac{44 x ^{3}}{44} = \frac{- 56}{44}

Divide the numbers

x^{3} = \frac{- 56}{44}

Divide the numbers

More Steps

Evaluate

\frac{- 56}{44}

Cancel out the common factor 4

\frac{- 14}{11}

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

- \frac{14}{11}

x^{3} = - \frac{14}{11}

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

3 x^{3} = 3 - \frac{14}{11}

Calculate

x = 3 - \frac{14}{11}

Solution

More Steps

Evaluate

3 - \frac{14}{11}

An odd root of a negative radicand is always a negative

- 3 \frac{14}{11}

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

- \frac{3 14}{3 11}

Multiply by the Conjugate

\frac{- 3 14 \times 3 1 1 ^{2}}{3 11 \times 3 1 1 ^{2}}

Simplify

\frac{- 3 14 \times 3 121}{3 11 \times 3 1 1 ^{2}}

Multiply the numbers

More Steps

Evaluate

- 314 \times 3121

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

- 3 14 \times 121

Calculate the product

- 31694

\frac{- 3 1694}{3 11 \times 3 1 1 ^{2}}

Multiply the numbers

More Steps

Evaluate

311 \times 3 1 1^{2}

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

3 11 \times 1 1^{2}

Calculate the product

3 1 1^{3}

Reduce the index of the radical and exponent with 3

11

\frac{- 3 1694}{11}

Calculate

- \frac{3 1694}{11}

x = - \frac{3 1694}{11}

Alternative Form

x \approx - 1.083707

Show Solution