Question

How do you solve the equation `x^2+6x+13=0` by completing the square?

Answer 1

`x = -3+-2i`

Explanation:

The difference of squares identity can be written:

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

Use this with `a=(x+3)` and `b=2i` as follows:

`0 = x^2+6x+13`

`color(white)(0) = x^2+6x+9+4`

`color(white)(0) = (x+3)^2-(2i)^2`

`color(white)(0) = ((x+3)-2i)((x+3)+2i)`

`color(white)(0) = (x+3-2i)(x+3+2i)`

Hence:

`x = -3+-2i`