To transform the quadratic into (x+p)^2=q we proceed as follows:
-3x^2+x+3=-9
this can be written as:
-3x^2+x=-9-3
-3x^2+x=-12
dividing through by -3 we get:
x^2-x/3=4
but c=(b/2a)^2
c=(1/36)
hence adding 1/36 on both sides of the equation we get:
x^2-x/3+1/36=4+1/36
factoring the LHS we get:
(x-1/6)(x-1/6)=145/36
(x-1/6)^2=145/36
The above expression is in the form of
(x+p)^2=q
where:
p=-1/6
q=145/36
