Question

How do you solve `x^2 + 4x - 9 = 0` by completing the square?

Answer 1

`x = -2+-sqrt(13)`

Explanation:

The difference of squares identity can be written:

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

Hence we find:

`0 = x^2+4x-9`

`color(white)(0) = x^2+4x+4-13`

`color(white)(0) = (x+2)^2-(sqrt(13))^2`

`color(white)(0) = ((x+2)-sqrt(13))((x+2)+sqrt(13))`

`color(white)(0) = (x+2-sqrt(13))(x+2+sqrt(13))`

Hence:

`x = -2+-sqrt(13)`