Ta có : \(36-\left(x+6\right)^2=\left(\sqrt{11}\right)^2=11\)
\(\Leftrightarrow36-\left(x+6\right)\left(x+6\right)=11\)
\(\Leftrightarrow x^2+12x+36=25\)
\(\Leftrightarrow x^2+12x+11=0\)
\(\Leftrightarrow x^2+x+11x+11=0\)
\(\Leftrightarrow x\left(x+1\right)+11\left(x+1\right)=0\)
\(\Leftrightarrow\left(x+1\right)\left(x+11\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-1\\x=-11\end{matrix}\right.\)
Vậy ...
Ta có: \(36-\left(x+6\right)^2=\left(\sqrt{11}\right)^2\)
\(\Leftrightarrow36-x^2-12x-36=11\)
\(\Leftrightarrow-x^2-12x-11=0\)
\(\Leftrightarrow x^2+12x+11=0\)
\(\Leftrightarrow x^2+x+11x+11=0\)
\(\Leftrightarrow x\left(x+1\right)+11\left(x+1\right)=0\)
\(\Leftrightarrow\left(x+1\right)\left(x+11\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x+1=0\\x+11=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-1\\x=-11\end{matrix}\right.\)
vậy: S={-1;-11}
