Find the Roots (Zeros) (x-6)^2-5=0

${(x - 6)}^{2} - 5 = 0$

Step 1

Add $5$ to both sides of the equation.

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

Step 2

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

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

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.

$x - 6 = \sqrt{5}$

Add $6$ to both sides of the equation.

$x = \sqrt{5} + 6$

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

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

Add $6$ to both sides of the equation.

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

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

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 8.23606797 \dots, 3.76393202 \dots$

Step 5