Question

Resolver a Equação:

(X - 2)^2 = 9

Answer 1

$(x-2)^2=9\\\\(x-2)(x-2)=9\\\\x^2-4x+4=9\\\\x^2-4x-5=0\\\\a=1\qquad\qquad\qquad{b}=-4\qquad\qquad\qquad{c}=-5\\\\\\x=\dfrac{-b\pm\sqrt{\Delta}}{2a}\longrightarrow{x}=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\\\x=\dfrac{-(-4)\pm\sqrt{(-4)^2-4\cdot(1)\cdot(-5)}}{2(1)}\\\\\\x=\dfrac{4\pm\sqrt{16+20}}{2}\\\\\\x=\dfrac{4\pm6}{2}\left\langle\begin{matrix}x'=5\\\\x''=-1\end{matrix}\right\\\\\\\\\boxed{S=\{-1,\ 5\}}$

Answer 2

vc pode resolver por Bhaskara desenvolvendo a expressão
 (x -2) * (x - 2), ou de forma mais prática, assim,

(x - 2)² = 9
(x - 2) = raiz de 9
x - 2 = + 3  ou  -3    (por ser raiz quadrada)
x= 3+2              x= -3 +2
x = 5                  x=-1
S={ -1 ; 5}