a) \(\left(x-3\right)^2=1\)
\(\Rightarrow\left[{}\begin{matrix}\left(x-3\right)^2=1^2\\\left(x-3\right)^2=-1^2\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x-3=1\\x-3=-1\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=4\\x=2\end{matrix}\right.\)
b) \(\left(x-\dfrac{1}{7}\right)^2=0\)
\(\Rightarrow x-\dfrac{1}{7}=0\)
\(\Rightarrow x=0+\dfrac{1}{7}\)
\(\Rightarrow x=\dfrac{1}{7}\)
c) \(\left(2x+3\right)^3=-27\)
\(\Rightarrow\left(2x+3\right)^3=\left(-3\right)^3\)
\(\Rightarrow2x+3=-3\)
\(\Rightarrow2x=-6\)
\(\Rightarrow x=-3\)
d) \(-\left(5+35x\right)^2=36\)
\(\Rightarrow\left[{}\begin{matrix}\left(-5-35x\right)^2=6^2\\\left(-5-35x\right)^2=\left(-6\right)^2\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}-5-35x=6\\-5-35x=-6\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}35x=-11\\35x=1\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=-\dfrac{11}{35}\\x=\dfrac{1}{35}\end{matrix}\right.\)
