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

Answer:

$(x +\frac{11}{6})^2=\frac{169}{36}$

Step-by-step explanation:

$3x^{2} +11x-4=0$

Divide the whole equation by 3

$x^{2} +\frac{11}{3}x-\frac{4}{3}=0$

Shift the constant term to the other side

$x^{2} +\frac{11}{3}x=\frac{4}{3}$

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

$x^{2} +\frac{11}{3}x+(\frac{11}{6})^2-(\frac{11}{6})^2=\frac{4}{3}$

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

$(x +\frac{11}{6})^2-\frac{121}{36}=\frac{4}{3}$

$(x +\frac{11}{6})^2=\frac{4}{3}+\frac{121}{36}$

$(x +\frac{11}{6})^2=\frac{169}{36}$

Hence Option B is correct . $(x +\frac{11}{6})^2=\frac{169}{36}$