Question

PLEASE HELP:

Which of the following equations would be the result of using completing the square to solve the equation 3x 2 + 11x - 4 = 0?

A:(x+11/3)^2=169/36
B:(x+11/6)^2=169/36
C:(x+11/6)^2=4/3

Answer 1

3x^2 + 11x - 4 = 0

x^2 + (11/3)x = 4/3

(x+11/6)^2 = 169/36

Answer is B.

Answer 2

`(x +(11)/(6))^2=(169)/(36)`

Explanation:

`3x^(2) +11x-4=0`

Divide the whole equation by 3

`x^(2) +(11)/(3)x-(4)/(3)=0`

Shift the constant term to the other side

`x^(2) +(11)/(3)x=(4)/(3)`

Add and subtract the square of half of the coefficient of x

`x^(2) +(11)/(3)x+((11)/(6))^2-((11)/(6))^2=(4)/(3)`

Using identity :
`a^2+2ab+b^2 =(a+b)^2`

`(x +(11)/(6))^2-(121)/(36)=(4)/(3)`

`(x +(11)/(6))^2=(4)/(3)+(121)/(36)`

`(x +(11)/(6))^2=(169)/(36)`

Hence Option B is correct .
`(x +(11)/(6))^2=(169)/(36)`