Solve the LQ problem only with fsolve$()$ command in Matlab $,$ i wish to see the proper setup $-$ thank you

In the LQ problem,

Min $L-\frac{1}{2}{x}^{T}Qx+\frac{1}{2}{u}^{T}Ru$

$s.t.f-x+Bu+c-0$

Define the Kalman gain

$K(B^{T}QB+R{)}^{-1}{B}^{T}Q$

Express $u^{*},{}^{*},x^{*},$ and $L^{*}$ in terms of $K.$

Using the new expressions, find $u^{*},{}^{*},x^{*},$ and $L^{*}$ for

Min $L-\frac{1}{2}{x}^T\left[\begin{array}{ccc}1& 0& 2\end{array}\right]$

$0x+\frac{1}{2}{u}^T\left[\begin{array}{ccc}2& 1& 1\end{array}\right]$

$1u$

$s.t.x-\left[\begin{array}{c}1\end{array}\right]$

$3+\left[\begin{array}{ccc}2& 2& 0\end{array}\right]$

$1u$

Finally, verify your results using MATLAB fmincon and fsolve.