Answer:
The correct answer is
option B : [tex](x+2)^2 = 16[/tex]
Step-by-step explanation:
Here the given quadratic equation is
[tex]x^2 +4x=12[/tex]
To complete the square we add both sides square of half of coefficient of x
we have
coefficient of x = 4
half of coefficient of [tex]x=\frac{4}{2} =2[/tex]
square of half of coefficient of x = [tex]2^2 = 4[/tex]
So we add 4 to both sides
[tex]x^2 +4x+ 4=12+4[/tex]
[tex]x^2+4x+4 = 16[/tex]
we have formula [tex]a^2+2ab+b^2 =(a+b)^2[/tex]
so using this formula we can write
[tex]x^2+4x+4 = x^2+4x+2^2 = (x+2)^2[/tex]
hence we have
[tex](x+2)^2 = 16[/tex]
