Determine a from the equation a*a=-4 if a*b=ab+5(a+b)+21 .

To determine the unknown from the given equation, we need
the definition of the operation of the composition law, definition which is given by the
expression from enunciation.

We have to put the given
expression in a more convenient
manner.

a*b=(a+5)(b+5)-4

Now,
we'll try to solve the equation
a*a=-4

a*a=(a+5)(a+5)-4

-4=a^2+10a+25
-
4

a^2+10a+25=0

(a+5)^2=0

a1=a2=-5