The square that I am supposed to complete is x^2+15x, and the answer is (x+15/2)^2. How does this answer account for the 15 separate from the 15^2? I am confuzzled. Same thing goes for x^2-7x the answer is (x-7/2)^2, but I don't see what happened to the original -7. Thanks for your help :-)

Question

The square that I am supposed to complete is x^2+15x, and the answer is (x+15/2)^2. How does this answer account for the 15 separate from the 15^2? I am confuzzled.  Same thing goes for x^2-7x the answer is (x-7/2)^2, but I don't see what happened to the original -7.  Thanks for your help :-)

drwls · Answer

Whenever you "complete the square" of a binomial that starts out x^2 + bx + __, the constant term that you want is c = (b/2)^2 and the resulting completed square will be (x + b/2)(x + b/2)