1) \(x^2-9=0\)
\(\Leftrightarrow x^2-3^2=0\)
\(\Leftrightarrow\left(x+3\right)\left(x-3\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-3=0\\x+3=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=3\\x=-3\end{matrix}\right.\)
4) \(4x^2-4=0\)
\(\Leftrightarrow4\left(x^2-1\right)=0\)
\(\Leftrightarrow4\left(x+1\right)\left(x-1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x+1=0\\x-1=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-1\\x=1\end{matrix}\right.\)
7) \(\left(3x+1\right)^2-16=0\)
\(\Leftrightarrow\left(3x+1\right)^2-4^2=0\)
\(\Leftrightarrow\left(3x+1-4\right)\left(3x+1+4\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}3x-3=0\\3x+5=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=1\\x=-\dfrac{5}{3}\end{matrix}\right.\)
10) \(\left(x+3\right)^2-x^2=45\)
\(\Leftrightarrow\left(x+3-x\right)\left(x+3+x\right)=45\)
\(\Leftrightarrow3\left(2x+3\right)=45\)
\(\Leftrightarrow2x+3=\dfrac{45}{3}\)
\(\Leftrightarrow2x+3=15\)
\(\Leftrightarrow2x=15-3\)
\(\Leftrightarrow2x=12\)
\(\Leftrightarrow x=\dfrac{12}{2}\)
\(\Leftrightarrow x=6\)
