\begin{tabular}{l} Solve \ $$ (x-5)^{2}=4 $$ \ \hline 80\end{tabular}

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Solve the equation $$ (x-5)^{2}=4 $$.
Solve the quadratic equation by following steps:
- step0: Solve using square roots:
  $$\left(x-5ight)^{2}=4$$
- step1: Simplify the expression:
  $$x-5=\pm \sqrt{4}$$
- step2: Simplify the expression:
  $$x-5=\pm 2$$
- step3: Separate into possible cases:
  $$\begin{align}&x-5=2\&x-5=-2\end{align}$$
- step4: Solve the equation:
  $$\begin{align}&x=7\&x=3\end{align}$$
- step5: Rewrite:
  $$x_{1}=3,x_{2}=7$$
The solutions to the equation $$(x-5)^{2}=4$$ are $$x=3$$ and $$x=7$$.
The solutions are $$x=3$$ and $$x=7$$.

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