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.
First you would divide 45 by 9 to see how many times it will double which gives you 5. Then, you would multiply 2000 by 2^5 (or just 2000x2x2x2x2x2) to get $64000
