completing the square

Question

completing the square, the expression x²+6x+116 equals (x+A)² +B, where 

A=

B=

Answer 1

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

Answer 2

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

Answer 3

A=6/2=3

(x+3)²=x²+6x+9

You want x²+6x+116 so add 116-9=107

B=107