Question

How do you complete the square to solve `x^2 + 4x = 12`?

Answer 1

`x^2 + 4x = 12`

To write the Left Hand Side as a Perfect Square, we add 4 to both sides:

`x^2 + 4x +4= 12+4`
`x^2 + 2*2*x + 2^2 = 16`
Using the Identity `color(blue)((a+b)^2 = a^2 + 2ab + b^2`, we get
`(x+2)^2 = 16`
`x + 2 = +sqrt16` or `x +2 = -sqrt16`
`x = + 4 -2 or -4 -2`
`color(blue)(x = 2 or x=-6`