a) \(x^2-8\text{ }x+16=0\)
\(\Leftrightarrow\left(x-4\right)^2=0\)
\(\Leftrightarrow x-4=0\Leftrightarrow x=4\)
b) \(\left(3x-2\right)^2-49=0\)
\(\Leftrightarrow\left(3x-2\right)^2=49\)
\(\Leftrightarrow\orbr{\begin{cases}3x-2=\sqrt{49}\\3x-2=-\sqrt{49}\end{cases}}\Rightarrow\orbr{\begin{cases}3x=9\\3x=-5\end{cases}}\Rightarrow\orbr{\begin{cases}x=3\\x=-\frac{5}{3}\end{cases}}\)
c) \(\left(10x-5\right)^2-9x^2=0\)
\(\Leftrightarrow\left(7x-5\right)\left(13x-5\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}7x-5=0\\13x-5=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=\frac{5}{7}\\x=\frac{5}{13}\end{cases}}\)
d) \(\left(7x+1\right)^2-25x^2=0\)
\(\Leftrightarrow\left(2x+1\right)\left(12x+1\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}2x+1=0\\12x+1=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=-\frac{1}{2}\\x=-\frac{1}{12}\end{cases}}\)