Solve Using the Square Root Property -2k^2=-162

$- 2 k^{2} = - 162$

Step 1

Divide each term in $- 2 k^{2} = - 162$ by $- 2$ and simplify.

Divide each term in $- 2 k^{2} = - 162$ by $- 2$ .

$\frac{- 2 k^{2}}{- 2} = \frac{- 162}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 k^{2}}{- 2} = \frac{- 162}{- 2}$

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

$k^{2} = \frac{- 162}{- 2}$

Simplify the right side.

Divide $- 162$ by $- 2$ .

$k^{2} = 81$

Step 2

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

$k = \pm \sqrt{81}$

Step 3

Simplify $\pm \sqrt{81}$ .

Rewrite $81$ as $9^{2}$ .

$k = \pm \sqrt{9^{2}}$

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

$k = \pm 9$

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.

$k = 9$

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

$k = - 9$

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

$k = 9, - 9$