Solve for g 4g^2=25

$4 g^{2} = 25$

Step 1

Divide each term in $4 g^{2} = 25$ by $4$ and simplify.

Divide each term in $4 g^{2} = 25$ by $4$ .

$\frac{4 g^{2}}{4} = \frac{25}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 g^{2}}{4} = \frac{25}{4}$

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

$g^{2} = \frac{25}{4}$

Step 2

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

$g = \pm \sqrt{\frac{25}{4}}$

Step 3

Simplify $\pm \sqrt{\frac{25}{4}}$ .

Rewrite $\sqrt{\frac{25}{4}}$ as $\frac{\sqrt{25}}{\sqrt{4}}$ .

$g = \pm \frac{\sqrt{25}}{\sqrt{4}}$

Simplify the numerator.

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

$g = \pm \frac{\sqrt{5^{2}}}{\sqrt{4}}$

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

$g = \pm \frac{5}{\sqrt{4}}$

Simplify the denominator.

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

$g = \pm \frac{5}{\sqrt{2^{2}}}$

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

$g = \pm \frac{5}{2}$

Step 4

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

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

$g = \frac{5}{2}$

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

$g = - \frac{5}{2}$

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

$g = \frac{5}{2}, - \frac{5}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$g = \frac{5}{2}, - \frac{5}{2}$

Decimal Form:

$g = 2.5, - 2.5$

Mixed Number Form:

$g = 2 \frac{1}{2}, - 2 \frac{1}{2}$