I am trying to solve an matrix equation of the form $$ X^2 + AX + B = 0 $$. After the multiplication of the matrices and after adding the matrices we get the following non-linear system of equations: $a^2+bc+a+c\:=\:7;$ $ab+bd+b+d=-1;$ $ac+cd-a+c=0;$ $d^2+bc-b+d=0$
I've tried factoring, tried to eliminate some of the unknowns but can't find a way to solve this system.
Can somebody help me with it ?
eliminating the variables $$b,c,d$$ we get for the following equation for $a$: $$\left( a+3 \right) \left( a-2 \right) \left( 14+5\,a \right) \left( -21+10\,a \right) =0$$ don't Forget to discuss the Special cases