Solve Using the Square Root Property (x-5)^2=6

${(x - 5)}^{2} = 6$

Step 1

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

$x - 5 = \pm \sqrt{6}$

Step 2

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.

$x - 5 = \sqrt{6}$

Add $5$ to both sides of the equation.

$x = \sqrt{6} + 5$

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

$x - 5 = - \sqrt{6}$

Add $5$ to both sides of the equation.

$x = - \sqrt{6} + 5$

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

$x = \sqrt{6} + 5, - \sqrt{6} + 5$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \sqrt{6} + 5, - \sqrt{6} + 5$

Decimal Form:

$x = 7.44948974 \dots, 2.55051025 \dots$