Question 75982
(x-5)^2 = 6 
{{{(sqrt(x-5))^2 = sqrt(6))}}} [take the square root of both sides]
{{{(x-5) = sqrt(6))}}} 

{{{(x-5+5) = 5+sqrt(6))}}} [solve for x]

 {{{(x) = 5+sqrt(6))}}}
or
{{{(x) = 7.4495))}}}
.
Check by plugging x=7.4495 back into the original equation
{{{(x-5)^2 = (6))}}}
{{{(7.4495-5)^2 = (6))}}}
(2.4495)^2=6
6.00=6 [checks out]