\(A=x\left(x+2\right)+2\left(x-\dfrac{3}{2}\right)\)
\(=x^2+2x+2x-3=x^2+4x-3\)
\(=\left(x^2+4x+4\right)-7=\left(x+2\right)^2-7\)
Vì \(\left(x+2\right)^2\ge0\forall x\Rightarrow\left(x+2\right)^2-7\ge-7\)
Dấu ''='' xảy ra khi x = -2
Vậy \(MIN_A=-7\Leftrightarrow x=-2\)