Algebra Examples

$7 x^{5} = - 84$

Step 1

Divide each term in $7 x^{5} = - 84$ by $7$ and simplify.

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Step 1.1

Divide each term in $7 x^{5} = - 84$ by $7$ .

$\frac{7 x^{5}}{7} = \frac{- 84}{7}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $7$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{7 x^{5}}{7} = \frac{- 84}{7}$

Step 1.2.1.2

Divide $x^{5}$ by $1$ .

$x^{5} = \frac{- 84}{7}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Divide $- 84$ by $7$ .

$x^{5} = - 12$

Step 2

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$x = \sqrt[5]{- 12}$

Step 3

Simplify $\sqrt[5]{- 12}$ .

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Step 3.1

Rewrite $- 12$ as ${(- 1)}^{5} \cdot 12$ .

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Step 3.1.1

Rewrite $- 12$ as $- 1 (12)$ .

$x = \sqrt[5]{- 1 (12)}$

Step 3.1.2

Rewrite $- 1$ as ${(- 1)}^{5}$ .

$x = \sqrt[5]{{(- 1)}^{5} \cdot 12}$

Step 3.2

Pull terms out from under the radical.

$x = - 1 \sqrt[5]{12}$

Step 3.3

Rewrite $- 1 \sqrt[5]{12}$ as $- \sqrt[5]{12}$ .

$x = - \sqrt[5]{12}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = - \sqrt[5]{12}$

Decimal Form:

$x = - 1.64375182 \dots$