Solve Using the Square Root Property -5x^2=-25

$- 5 x^{2} = - 25$

Step 1

Divide each term in $- 5 x^{2} = - 25$ by $- 5$ and simplify.

Divide each term in $- 5 x^{2} = - 25$ by $- 5$ .

$\frac{- 5 x^{2}}{- 5} = \frac{- 25}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 x^{2}}{- 5} = \frac{- 25}{- 5}$

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

$x^{2} = \frac{- 25}{- 5}$

Simplify the right side.

Divide $- 25$ by $- 5$ .

$x^{2} = 5$

Step 2

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

$x = \pm \sqrt{5}$

Step 3

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.

$x = \sqrt{5}$

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

$x = - \sqrt{5}$

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

$x = \sqrt{5}, - \sqrt{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \sqrt{5}, - \sqrt{5}$

Decimal Form:

$x = 2.23606797 \dots, - 2.23606797 \dots$