Question

What equation results from completing the square and then factoring x^2+4x=12?

A) (x+2)^2=10
B) (x+2)^2=14
C) (x+2)^2=16
D) (x+2)^2=8

Answer 1

x² + 4x =12
x² + 4x = 16 - 4
x² + 4x + 4 = 16
(x+2)² = 16

Answer: C.

Answer 2

The correct answer is

option B :
`(x+2)^2 = 16`

Explanation:

Here the given quadratic equation is

`x^2 +4x=12`

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
`x=(4)/(2) =2`

square of half of coefficient of x =
`2^2 = 4`

So we add 4 to both sides

`x^2 +4x+ 4=12+4`

`x^2+4x+4 = 16`

we have formula
`a^2+2ab+b^2 =(a+b)^2`

so using this formula we can write

`x^2+4x+4 = x^2+4x+2^2 = (x+2)^2`

hence we have

`(x+2)^2 = 16`