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
