Basic Math Examples

$a = 25 m^{2}$

Step 1

Rewrite the equation as

$25 m^{2} = a$ .

$25 m^{2} = a$

Step 2

Divide each term in

$25 m^{2} = a$ by

$25$ and simplify.

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Step 2.1

Divide each term in

$25 m^{2} = a$ by

$25$ .

$\frac{25 m^{2}}{25} = \frac{a}{25}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of

$25$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{25 m^{2}}{25} = \frac{a}{25}$

Step 2.2.1.2

Divide

$m^{2}$ by

$1$ .

$m^{2} = \frac{a}{25}$

Step 3

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

$m = \pm \sqrt{\frac{a}{25}}$

Step 4

Simplify

$\pm \sqrt{\frac{a}{25}}$ .

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Step 4.1

Rewrite

$\frac{a}{25}$ as

${(\frac{1}{5})}^{2} a$ .

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Step 4.1.1

Factor the perfect power

$1^{2}$ out of

$a$ .

$m = \pm \sqrt{\frac{1^{2} a}{25}}$

Step 4.1.2

Factor the perfect power

$5^{2}$ out of

$25$ .

$m = \pm \sqrt{\frac{1^{2} a}{5^{2} \cdot 1}}$

Step 4.1.3

Rearrange the fraction

$\frac{1^{2} a}{5^{2} \cdot 1}$ .

$m = \pm \sqrt{{(\frac{1}{5})}^{2} a}$

Step 4.2

Pull terms out from under the radical.

$m = \pm \frac{1}{5} \sqrt{a}$

Step 4.3

Combine

$\frac{1}{5}$ and

$\sqrt{a}$ .

$m = \pm \frac{\sqrt{a}}{5}$

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.

$m = \frac{\sqrt{a}}{5}$

Step 5.2

Next, use the negative value of the

$\pm$ to find the second solution.

$m = - \frac{\sqrt{a}}{5}$

Step 5.3

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

$m = \frac{\sqrt{a}}{5}$

$m = - \frac{\sqrt{a}}{5}$

$m = \frac{\sqrt{a}}{5}$

$m = - \frac{\sqrt{a}}{5}$