^{2}+6x+116 equals (x+A)

^{2 }+B, where

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

A=

B=

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when you complete the square you have to focus on the coefficient for x (not x^{2}, 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 x^{2} + 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:

Michael F. | Mathematics TutorMathematics Tutor

A=6/2=3

(x+3)²=x²+6x+9

You want x²+6x+116 so add 116-9=107

B=107

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