a) \(x^2-2x+1=25\)
\(\Rightarrow x^2-2x+1-25=0\)
\(\Rightarrow x^2-2x.1+1^2-5^2=0\)
\(\Rightarrow\left(x-1\right)^2-5^2=0\)
\(\Rightarrow\left(x-1-5\right)\left(x-1+5\right)=0\)
\(\Rightarrow\left(x-6\right)\left(x+4\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x-6=0\\x+4=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=6\\x=\left(-4\right)\end{cases}}\)
b) \(\left(5x+1\right)^2-\left(5x-3\right)\left(5x+3\right)30\)
\(\Rightarrow\left(5x\right)^2+2.5x.1+1^2-\left(25x^2-9\right)-30=0\)
\(\Rightarrow25x^2+10x+1-25x^2+9-30=0\)
\(\Rightarrow\left(25x^2-25x^2\right)+10x+\left(1+9-30\right)=0\)
\(\Rightarrow10x-20=0\)
\(\Rightarrow10x=20\)
\(\Rightarrow x=2\)
