Basic Math Examples

$81 b^{2} - 1 = 0$

Step 1

Add $1$ to both sides of the equation.

$81 b^{2} = 1$

Step 2

Divide each term in $81 b^{2} = 1$ by $81$ and simplify.

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Step 2.1

Divide each term in $81 b^{2} = 1$ by $81$ .

$\frac{81 b^{2}}{81} = \frac{1}{81}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $81$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{81 b^{2}}{81} = \frac{1}{81}$

Step 2.2.1.2

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

$b^{2} = \frac{1}{81}$

Step 3

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

$b = \pm \sqrt{\frac{1}{81}}$

Step 4

Simplify $\pm \sqrt{\frac{1}{81}}$ .

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Step 4.1

Rewrite $\sqrt{\frac{1}{81}}$ as $\frac{\sqrt{1}}{\sqrt{81}}$ .

$b = \pm \frac{\sqrt{1}}{\sqrt{81}}$

Step 4.2

Any root of $1$ is $1$ .

$b = \pm \frac{1}{\sqrt{81}}$

Step 4.3

Simplify the denominator.

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Step 4.3.1

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

$b = \pm \frac{1}{\sqrt{9^{2}}}$

Step 4.3.2

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

$b = \pm \frac{1}{9}$

Step 5

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

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Step 5.1

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

$b = \frac{1}{9}$

Step 5.2

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

$b = - \frac{1}{9}$

Step 5.3

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

$b = \frac{1}{9}, - \frac{1}{9}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$b = \frac{1}{9}, - \frac{1}{9}$

Decimal Form:

$b = 0.\overline{1}, - 0.\overline{1}$