Solve Using the Square Root Property 2x^2-5=-205

$2 x^{2} - 5 = - 205$

Step 1

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

Add $5$ to both sides of the equation.

$2 x^{2} = - 205 + 5$

Add $- 205$ and $5$ .

$2 x^{2} = - 200$

Step 2

Divide each term in $2 x^{2} = - 200$ by $2$ and simplify.

Divide each term in $2 x^{2} = - 200$ by $2$ .

$\frac{2 x^{2}}{2} = \frac{- 200}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x^{2}}{2} = \frac{- 200}{2}$

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

$x^{2} = \frac{- 200}{2}$

Simplify the right side.

Divide $- 200$ by $2$ .

$x^{2} = - 100$

Step 3

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

$x = \pm \sqrt{- 100}$

Step 4

Simplify $\pm \sqrt{- 100}$ .

Rewrite $- 100$ as $- 1 (100)$ .

$x = \pm \sqrt{- 1 (100)}$

Rewrite $\sqrt{- 1 (100)}$ as $\sqrt{- 1} \cdot \sqrt{100}$ .

$x = \pm \sqrt{- 1} \cdot \sqrt{100}$

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

$x = \pm i \cdot \sqrt{100}$

Rewrite $100$ as $10^{2}$ .

$x = \pm i \cdot \sqrt{10^{2}}$

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

$x = \pm i \cdot 10$

Move $10$ to the left of $i$ .

$x = \pm 10 i$

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.

$x = 10 i$

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

$x = - 10 i$

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

$x = 10 i, - 10 i$