Solve for m square root of 36/9=1/3m^2-10

$\sqrt{\frac{36}{9}} = \frac{1}{3} m^{2} - 10$

Step 1

Rewrite the equation as $\frac{1}{3} m^{2} - 10 = \sqrt{\frac{36}{9}}$ .

$\frac{1}{3} m^{2} - 10 = \sqrt{\frac{36}{9}}$

Step 2

Combine $\frac{1}{3}$ and $m^{2}$ .

$\frac{m^{2}}{3} - 10 = \sqrt{\frac{36}{9}}$

Step 3

Simplify $\sqrt{\frac{36}{9}}$ .

Divide $36$ by $9$ .

$\frac{m^{2}}{3} - 10 = \sqrt{4}$

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

$\frac{m^{2}}{3} - 10 = \sqrt{2^{2}}$

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

$\frac{m^{2}}{3} - 10 = 2$

Step 4

Move all terms not containing $m$ to the right side of the equation.

Add $10$ to both sides of the equation.

$\frac{m^{2}}{3} = 2 + 10$

Add $2$ and $10$ .

$\frac{m^{2}}{3} = 12$

Step 5

Multiply both sides of the equation by $3$ .

$3 \frac{m^{2}}{3} = 3 \cdot 12$

Step 6

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$3 \frac{m^{2}}{3} = 3 \cdot 12$

Rewrite the expression.

$m^{2} = 3 \cdot 12$

Simplify the right side.

Multiply $3$ by $12$ .

$m^{2} = 36$

Step 7

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

$m = \pm \sqrt{36}$

Step 8

Simplify $\pm \sqrt{36}$ .

Rewrite $36$ as $6^{2}$ .

$m = \pm \sqrt{6^{2}}$

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

$m = \pm 6$

Step 9

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.

$m = 6$

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

$m = - 6$

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

$m = 6, - 6$

Solve for m square root of 36/9=1/3m^2-10

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