The discriminant is equal to b^2-4ac where the equation is of the form ax^2+bx+c=0. In this question, a=1, b=2 and c=-2. Therefore, the discriminant is equal to (2^2)-(4*1*-2)=4-(-8)=12
Completing the square on the left gives (x+6)^2 which when expanded gives x^2+12x+36. Therefore we must take away the 36 from each side to be left with just x^2+12x on the left. Therefore, the answer is -36.
We have the equation x^2-12x+36=0. First we look at the 'c' value which is 36 and think which number we can square to find it. In this case it is either 6 or -6. Trying each gives (x-6)^2=x^2-12x+36 and (x+6)^2=x^2+12x+36. We can see here the (x-6)^2 is the correct factorization of the left hand side. Therefore, we now have the equation (x-6)^2=0. For this to be true, the bracket must equal 0 and so x must equal 6. Therefore, the answer is 6.
We have the equation x^2-x=14. We must rearrange this equation so we have 0 on the right hand side. To do this we must subtract 14 from each side. This gives x^2-x-14=0. Once again, the equation is of the form ax^2+bx+c=0 and so we see that here, a=1, b=-1 and c=-14.