\(A=x\left(x+2\right)+2\left(x-\frac{3}{2}\right)\)
\(=x^2+2x+2x-3\)
\(=x^2+4x-3\)
\(=\left(x^2+4x+4\right)-7\)
\(=\left(x+2\right)^2-7\ge-7\)
Dấu "=" xảy ra khi \(\left(x+2\right)^2=0\Rightarrow x+2=0\Rightarrow x=-2\)
Vậy \(Min_A=-7\) khi \(x=-2\)