Optimizing the above equation, that is
\nabla f = 0 = \boldsymbol{A}\boldsymbol{x}-\boldsymbol{b},which leads to a simple matrix-inversion problem
\boldsymbol{x}=\boldsymbol{A}^{-1}\boldsymbol{b}.This problem is easy to solve since we can calculate the inverse. Alternatively, we can solve the two coupled equations with two unknowns
\frac{\partial f}{\partial x_1}=2x_1+x_2-5=0,and
\frac{\partial f}{\partial x_2}=x_1+20x_2-3=0,with solutions x_1=97/39 and x_2=1/39 .