Answer:
x= 14
Step-by-step explanation:
sqrt( x-5) = x-11
Square each side
(sqrt( x-5))^2 = (x-11)^2
x-5 = x^2 - 22x +121
Subtract (x-5) from each side
x-5-x+5 = x^2 -22x +121 -x+5
0 = x^2 -23x +126
Factor
0 = ( x-14) ( x-9)
Using the zero product property
x-14 = 0 x-9=0
x=14 x=9
Check the solutions
sqrt( x-5) = x-11
sqrt( 14-5) = 14-11
sqrt(9) = 3
3=3
solution
sqrt( x-5) = x-11
sqrt(9-5) = 9-11
sqrt(4) =-2
2 = -2
not a solution
