Search 75,087 tutors
FIND TUTORS
Ask a question
0 0

completing the square

Tutors, please sign in to answer this question.

3 Answers

when you complete the square you have to focus on  the coefficient for x (not x2, just the regular x)
 
in your case its its 6 --> what you want to do is cut it in half (3) and then square it, thats where the 9 comes from.
 
ideally, you would have x2 + 6x + 9, but it has to be +116 at the end instead b/c thats just what your question is
 
so lets be creative and split the 116 into 9 and 107 ---> you have to do this b/c it has to total 116 and you want to have that 9 in there
 
x2 + 6x + 9 + 107
 
you can factor out the orange part into (x+3)2
 
so its
 
(x+3)2 +107     so a is 3 and b is 107
X^2 + 6X + 116 = (X + A)^2 + B
 
Divide 6 by 2 and you get 3. When you square the 3, you get 9. Therefore the square X^2 + 6X + 9 is formed because it is the square of X + 3. Therefore the completed square of X^2 + 6X + 116 would be:
 
(X + 3)^2 + 107
 
A = 3
 
B = 107