Question

How do you solve the equation `x^2+4x+2=0` by completing the square?

Answer 1

`x = -2+-sqrt(2)`

Explanation:

The difference of squares identity can be written:

`a_2-b^2 = (a-b)(a+b)`

Complete the square then use this with `a=(x+2)` and `b=sqrt(2)` as follows:

`0 = x^2+4x+2`

`color(white)(0) = x^2+4x+4-2`

`color(white)(0) = (x+2)^2-(sqrt(2))^2`

`color(white)(0) = ((x+2)-sqrt(2))((x+2)+sqrt(2))`

`color(white)(0) = (x+2-sqrt(2))(x+2+sqrt(2))`

Hence:

`x = -2+-sqrt(2)`