What number must be added to both sides of the equation to complete the square?

X^2+12x=-6

a) - 144

b) 36

c) - 36

d) 144

First consider (x+c) ^2 where c is just a random constant. if we expand this by foil (which is distributive property twice), we get x^2 + 2cx + c^2. we want to find c^2 and to do that, we can first find c. we can find c by looking at the 2cx term. this term should match with 12x, so therefore 2c = 12 so c = 6. this also implies that c^2 = 36.

note that for this problem i was working backwards which is a very powerful problem solving tool: start with what you want to attain, and then see how you can go from where you are now to get to your destination.

let me know if you have any questions!