Solve for m -158=-8-5m^2

$- 158 = - 8 - 5 m^{2}$

Step 1

Rewrite the equation as $- 8 - 5 m^{2} = - 158$ .

$- 8 - 5 m^{2} = - 158$

Step 2

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

Add $8$ to both sides of the equation.

$- 5 m^{2} = - 158 + 8$

Add $- 158$ and $8$ .

$- 5 m^{2} = - 150$

Step 3

Divide each term in $- 5 m^{2} = - 150$ by $- 5$ and simplify.

Divide each term in $- 5 m^{2} = - 150$ by $- 5$ .

$\frac{- 5 m^{2}}{- 5} = \frac{- 150}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 m^{2}}{- 5} = \frac{- 150}{- 5}$

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

$m^{2} = \frac{- 150}{- 5}$

Simplify the right side.

Divide $- 150$ by $- 5$ .

$m^{2} = 30$

Step 4

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

$m = \pm \sqrt{30}$

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.

$m = \sqrt{30}$

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

$m = - \sqrt{30}$

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

$m = \sqrt{30}, - \sqrt{30}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$m = \sqrt{30}, - \sqrt{30}$

Decimal Form:

$m = 5.47722557 \dots, - 5.47722557 \dots$