Solve Using the Square Root Property x^2-47=0

$x^{2} - 47 = 0$

Step 1

Add $47$ to both sides of the equation.

$x^{2} = 47$

Step 2

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

$x = \pm \sqrt{47}$

Step 3

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.

$x = \sqrt{47}$

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

$x = - \sqrt{47}$

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

$x = \sqrt{47}, - \sqrt{47}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \sqrt{47}, - \sqrt{47}$

Decimal Form:

$x = 6.85565460 \dots, - 6.85565460 \dots$