Algebra Examples

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

Step 1

Rewrite the equation as $\frac{b^{2}}{25} = c$ .

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

Step 2

Multiply both sides of the equation by $25$ .

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

Step 3

Simplify the left side.

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Step 3.1

Cancel the common factor of $25$ .

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Step 3.1.1

Cancel the common factor.

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

Step 3.1.2

Rewrite the expression.

$b^{2} = 25 c$

Step 4

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

$b = \pm \sqrt{25 c}$

Step 5

Simplify $\pm \sqrt{25 c}$ .

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Step 5.1

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

$b = \pm \sqrt{5^{2} c}$

Step 5.2

Pull terms out from under the radical.

$b = \pm 5 \sqrt{c}$

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.

$b = 5 \sqrt{c}$

Step 6.2

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

$b = - 5 \sqrt{c}$

Step 6.3

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

$b = 5 \sqrt{c}$

$b = - 5 \sqrt{c}$

$b = 5 \sqrt{c}$

$b = - 5 \sqrt{c}$