Solve Using the Square Root Property 2x^2-38=0

$2 x^{2} - 38 = 0$

Step 1

Add $38$ to both sides of the equation.

$2 x^{2} = 38$

Step 2

Divide each term in $2 x^{2} = 38$ by $2$ and simplify.

Divide each term in $2 x^{2} = 38$ by $2$ .

$\frac{2 x^{2}}{2} = \frac{38}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x^{2}}{2} = \frac{38}{2}$

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

$x^{2} = \frac{38}{2}$

Simplify the right side.

Divide $38$ by $2$ .

$x^{2} = 19$

Step 3

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

$x = \pm \sqrt{19}$

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.

$x = \sqrt{19}$

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

$x = - \sqrt{19}$

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

$x = \sqrt{19}, - \sqrt{19}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \sqrt{19}, - \sqrt{19}$

Decimal Form:

$x = 4.35889894 \dots, - 4.35889894 \dots$