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# completing the square

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

### 3 Answers by Expert Tutors

Justin L. | A Personalized Approach to a Standardized EducationA Personalized Approach to a Standardize...
5.0 5.0 (7 lesson ratings) (7)
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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
4.9 4.9 (220 lesson ratings) (220)
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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
Michael F. | Mathematics TutorMathematics Tutor
4.7 4.7 (7 lesson ratings) (7)
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A=6/2=3
(x+3)²=x²+6x+9
You want x²+6x+116 so add 116-9=107
B=107