Verified Answer :

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

(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.

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