Question

What number must be added to the expression below to complete the square? x^2 + x

I wouldn't know how to start so go through it with me if you'd like!

Answer 1

add 1/4

Answer 2

(x+1/2)^2 is what you are looking for

1/2 (x) + 1/2(x) = x and 1/2 * 1/2 = 1/4

Answer 3

There's an easier method. Just divide the coefficient of the second number, x, which is one, by two. So 1/2. Then square it to get 1/4. Trust me. This method ALWAYS works.

Answer 4

Ax^2+Bx+C right ?
Well (B/2)^2 will always equal C.

Answer 5

Hope this helps! :)

Answer 6

you want (x + b)^2 = x^2 + 1x + c where b and c are real numbers to be found
expanding the left hand side:

x^2 + 2bx + b^2 = x^2 + 1x + c

equating individual terms

2b = 1...........(1)

b^2 = c.........(2)


from (1):- b = 1/2
now we substitute for b in equation (2):-
(1/2)^2 = c

c = 1/4
c = a/4



therefor

Answer 7

so we have x^2 + (1/2)x + 1/4 = ( x +1/2)^2

Answer 8

I dont know what happened to my posts - they got all mixed up

Answer 9

yes you are right Joylin - I went through it from basic principles because it seemed to me thats what johnny621 wanted.

Answer 10

I just elaborated and offered him a formula that'll always help him. You're method is fine as well.

Answer 11

So it's 1/4? Thank you all for the help! Also extra thanks for going through the method!