[latex](x-2)^2=49\iff x-2=\sqrt{49}\ or\ x-2=-\sqrt{49}\\\\x-2=7\ or\ x-2=-7\\\\x=7+2\ or\ x=-7+2\\\\x=9\ or\ x=-5\\\\Answer:x\in\{-5;\ 9\}[/latex]

(x - 2)² = 49 x² - 2x - 2x + 4 = 49 x² - 4x = 45 x² - 2x = 45 + (- 2)² x² - 2x = 45 + 4 (x - 2)² = 49 x - 2 = 7 x = 7 + 2, x = 9 x = - 7 + 2, x = - 5 Answer: 9 or the fifth choice. x is also - 5.