Solve Using the Square Root Property 2x^2+5=19

$2 x^{2} + 5 = 19$

Step 1

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

Subtract $5$ from both sides of the equation.

$2 x^{2} = 19 - 5$

Subtract $5$ from $19$ .

$2 x^{2} = 14$

Step 2

Divide each term in $2 x^{2} = 14$ by $2$ and simplify.

Divide each term in $2 x^{2} = 14$ by $2$ .

$\frac{2 x^{2}}{2} = \frac{14}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x^{2}}{2} = \frac{14}{2}$

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

$x^{2} = \frac{14}{2}$

Simplify the right side.

Divide $14$ by $2$ .

$x^{2} = 7$

Step 3

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

$x = \pm \sqrt{7}$

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.

$x = \sqrt{7}$

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

$x = - \sqrt{7}$

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

$x = \sqrt{7}, - \sqrt{7}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \sqrt{7}, - \sqrt{7}$

Decimal Form:

$x = 2.64575131 \dots, - 2.64575131 \dots$