Answer:
x = 5±sqrt(3)
Step-by-step explanation:
(x-5)^2=3
Take the square root of each side
sqrt((x-5)^2)=±sqrt(3)
x-5 = ±sqrt(3)
Add 5 to each side
x-5 +5= 5±sqrt(3)
[tex]\huge\boxed{x=5-\sqrt3\ \vee\ x=5+\sqrt3}[/tex]
[tex](x-5)^2=3\iff x-5=\pm\sqrt3\qquad\text{add 5 to both sides}\\\\x-5+5=-\sqrt3+5\ \vee\ x-5+5=\sqrt3+5\\\\x=5-\sqrt3\ \vee\ x=5+\sqrt3[/tex]
