Solve for m 2m^2+10=0

$2 m^{2} + 10 = 0$

Step 1

Subtract $10$ from both sides of the equation.

$2 m^{2} = - 10$

Step 2

Divide each term in $2 m^{2} = - 10$ by $2$ and simplify.

Divide each term in $2 m^{2} = - 10$ by $2$ .

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

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

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

Simplify the right side.

Divide $- 10$ by $2$ .

$m^{2} = - 5$

Step 3

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

$m = \pm \sqrt{- 5}$

Step 4

Simplify $\pm \sqrt{- 5}$ .

Rewrite $- 5$ as $- 1 (5)$ .

$m = \pm \sqrt{- 1 (5)}$

Rewrite $\sqrt{- 1 (5)}$ as $\sqrt{- 1} \cdot \sqrt{5}$ .

$m = \pm \sqrt{- 1} \cdot \sqrt{5}$

Rewrite $\sqrt{- 1}$ as $i$ .

$m = \pm i \sqrt{5}$

Step 5

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.

$m = i \sqrt{5}$

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

$m = - i \sqrt{5}$

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

$m = i \sqrt{5}, - i \sqrt{5}$