Pre-Algebra Examples

$81 x^{2} = 16$

Step 1

Divide each term in $81 x^{2} = 16$ by $81$ and simplify.

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Step 1.1

Divide each term in $81 x^{2} = 16$ by $81$ .

$\frac{81 x^{2}}{81} = \frac{16}{81}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $81$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{81 x^{2}}{81} = \frac{16}{81}$

Step 1.2.1.2

Divide $x^{2}$ by $1$ .

$x^{2} = \frac{16}{81}$

Step 2

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

$x = \pm \sqrt{\frac{16}{81}}$

Step 3

Simplify $\pm \sqrt{\frac{16}{81}}$ .

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Step 3.1

Rewrite $\sqrt{\frac{16}{81}}$ as $\frac{\sqrt{16}}{\sqrt{81}}$ .

$x = \pm \frac{\sqrt{16}}{\sqrt{81}}$

Step 3.2

Simplify the numerator.

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Step 3.2.1

Rewrite $16$ as $4^{2}$ .

$x = \pm \frac{\sqrt{4^{2}}}{\sqrt{81}}$

Step 3.2.2

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm \frac{4}{\sqrt{81}}$

Step 3.3

Simplify the denominator.

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Step 3.3.1

Rewrite $81$ as $9^{2}$ .

$x = \pm \frac{4}{\sqrt{9^{2}}}$

Step 3.3.2

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm \frac{4}{9}$

Step 4

The complete solution is the result of both the positive and negative portions of the solution.

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Step 4.1

First, use the positive value of the $\pm$ to find the first solution.

$x = \frac{4}{9}$

Step 4.2

Next, use the negative value of the $\pm$ to find the second solution.

$x = - \frac{4}{9}$

Step 4.3

The complete solution is the result of both the positive and negative portions of the solution.

$x = \frac{4}{9}, - \frac{4}{9}$