Basic Math Examples

$\frac{16 b^{2}}{9} + b^{2} = 1296$

Step 1

Simplify $\frac{16 b^{2}}{9} + b^{2}$ .

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Step 1.1

To write $b^{2}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{16 b^{2}}{9} + b^{2} \cdot \frac{9}{9} = 1296$

Step 1.2

Simplify terms.

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Step 1.2.1

Combine $b^{2}$ and $\frac{9}{9}$ .

$\frac{16 b^{2}}{9} + \frac{b^{2} \cdot 9}{9} = 1296$

Step 1.2.2

Combine the numerators over the common denominator.

$\frac{16 b^{2} + b^{2} \cdot 9}{9} = 1296$

Step 1.3

Simplify the numerator.

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Step 1.3.1

Move $9$ to the left of $b^{2}$ .

$\frac{16 b^{2} + 9 \cdot b^{2}}{9} = 1296$

Step 1.3.2

Add $16 b^{2}$ and $9 b^{2}$ .

$\frac{25 b^{2}}{9} = 1296$

Step 2

Multiply both sides of the equation by $\frac{9}{25}$ .

$\frac{9}{25} \cdot \frac{25 b^{2}}{9} = \frac{9}{25} \cdot 1296$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $\frac{9}{25} \cdot \frac{25 b^{2}}{9}$ .

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Step 3.1.1.1

Combine.

$\frac{9 (25 b^{2})}{25 \cdot 9} = \frac{9}{25} \cdot 1296$

Step 3.1.1.2

Cancel the common factor of $9$ .

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Step 3.1.1.2.1

Cancel the common factor.

$\frac{9 (25 b^{2})}{25 \cdot 9} = \frac{9}{25} \cdot 1296$

Step 3.1.1.2.2

Rewrite the expression.

$\frac{25 b^{2}}{25} = \frac{9}{25} \cdot 1296$

Step 3.1.1.3

Cancel the common factor of $25$ .

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Step 3.1.1.3.1

Cancel the common factor.

$\frac{25 b^{2}}{25} = \frac{9}{25} \cdot 1296$

Step 3.1.1.3.2

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

$b^{2} = \frac{9}{25} \cdot 1296$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $\frac{9}{25} \cdot 1296$ .

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Step 3.2.1.1

Combine $\frac{9}{25}$ and $1296$ .

$b^{2} = \frac{9 \cdot 1296}{25}$

Step 3.2.1.2

Multiply $9$ by $1296$ .

$b^{2} = \frac{11664}{25}$

Step 4

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

$b = \pm \sqrt{\frac{11664}{25}}$

Step 5

Simplify $\pm \sqrt{\frac{11664}{25}}$ .

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Step 5.1

Rewrite $\sqrt{\frac{11664}{25}}$ as $\frac{\sqrt{11664}}{\sqrt{25}}$ .

$b = \pm \frac{\sqrt{11664}}{\sqrt{25}}$

Step 5.2

Simplify the numerator.

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Step 5.2.1

Rewrite $11664$ as $108^{2}$ .

$b = \pm \frac{\sqrt{108^{2}}}{\sqrt{25}}$

Step 5.2.2

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

$b = \pm \frac{108}{\sqrt{25}}$

Step 5.3

Simplify the denominator.

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Step 5.3.1

Rewrite $25$ as $5^{2}$ .

$b = \pm \frac{108}{\sqrt{5^{2}}}$

Step 5.3.2

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

$b = \pm \frac{108}{5}$

Step 6

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

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Step 6.1

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

$b = \frac{108}{5}$

Step 6.2

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

$b = - \frac{108}{5}$

Step 6.3

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

$b = \frac{108}{5}, - \frac{108}{5}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$b = \frac{108}{5}, - \frac{108}{5}$

Decimal Form:

$b = 21.6, - 21.6$

Mixed Number Form:

$b = 21 \frac{3}{5}, - 21 \frac{3}{5}$