Solve Using the Square Root Property 2x^2-28=0

$2 x^{2} - 28 = 0$

Step 1

Add $28$ to both sides of the equation.

$2 x^{2} = 28$

Step 2

Divide each term in $2 x^{2} = 28$ by $2$ and simplify.

Divide each term in $2 x^{2} = 28$ by $2$ .

$\frac{2 x^{2}}{2} = \frac{28}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x^{2}}{2} = \frac{28}{2}$

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

$x^{2} = \frac{28}{2}$

Simplify the right side.

Divide $28$ by $2$ .

$x^{2} = 14$

Step 3

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

$x = \pm \sqrt{14}$

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.

$x = \sqrt{14}$

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

$x = - \sqrt{14}$

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

$x = \sqrt{14}, - \sqrt{14}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \sqrt{14}, - \sqrt{14}$

Decimal Form:

$x = 3.74165738 \dots, - 3.74165738 \dots$