helpppppp , quick answer with work pleaseeee

Answer:
Step-by-step explanation:
[tex]\sqrt{x-2}+8=x\\\\\sqrt{x-2}=x-8\\[/tex]
Square both sides,
[tex]x-2=(x-8)^{2}\\\\x-2=x^{2}-2*x*8+8^{2}\\\\x-2=x^{2}-16x+64\\\\x^{2}-16x+64=x-2\\\\x^{2}-16x+64-x+2=0\\\\x^{2}-17x+66=0[/tex]
Sum = - 17
Product = 66
Factors = -6 , -11
x² - 6x -11x + (-6)*(-11) = 0
x(x - 6) -11(x - 6) = 0
(x-6) (x - 11) = 0
x -6 = 0 ; x - 11 = 0
x = 6 ; x =11
Here, x = 6 is a extraneous solution