Solve Using the Square Root Property 2x^2+50=-166

$2 x^{2} + 50 = - 166$

Step 1

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

Subtract $50$ from both sides of the equation.

$2 x^{2} = - 166 - 50$

Subtract $50$ from $- 166$ .

$2 x^{2} = - 216$

Step 2

Divide each term in $2 x^{2} = - 216$ by $2$ and simplify.

Divide each term in $2 x^{2} = - 216$ by $2$ .

$\frac{2 x^{2}}{2} = \frac{- 216}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x^{2}}{2} = \frac{- 216}{2}$

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

$x^{2} = \frac{- 216}{2}$

Simplify the right side.

Divide $- 216$ by $2$ .

$x^{2} = - 108$

Step 3

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

$x = \pm \sqrt{- 108}$

Step 4

Simplify $\pm \sqrt{- 108}$ .

Rewrite $- 108$ as $- 1 (108)$ .

$x = \pm \sqrt{- 1 (108)}$

Rewrite $\sqrt{- 1 (108)}$ as $\sqrt{- 1} \cdot \sqrt{108}$ .

$x = \pm \sqrt{- 1} \cdot \sqrt{108}$

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

$x = \pm i \cdot \sqrt{108}$

Rewrite $108$ as $6^{2} \cdot 3$ .

Factor $36$ out of $108$ .

$x = \pm i \cdot \sqrt{36 (3)}$

Rewrite $36$ as $6^{2}$ .

$x = \pm i \cdot \sqrt{6^{2} \cdot 3}$

Pull terms out from under the radical.

$x = \pm i \cdot (6 \sqrt{3})$

Move $6$ to the left of $i$ .

$x = \pm 6 i \sqrt{3}$

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.

$x = 6 i \sqrt{3}$

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

$x = - 6 i \sqrt{3}$

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

$x = 6 i \sqrt{3}, - 6 i \sqrt{3}$

Solve Using the Square Root Property 2x^2+50=-166

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