Question

How do you solve using the completing the square method `x^2+2x-5=0`?

Answer 1

`x=-1-sqrt6` or `x=-1+sqrt6`

Explanation:

`x^2+2x-5=0`

Now, recalling the identity `(x+a)^2=x^2+2ax+a^2` and comparing it with `x^2+2x`, we need to add and subtract `(2/1)^2` to complete square. Hence `x^2+2x-5=0` is

`x^2+2x+1-1-5=0` or

`(x^2+2x+1)-6=0` or

`(x+1)^2-(sqrt6)^2` or

`(x+1+sqrt6)(x+1-sqrt6)=0`

i.e. `x=-1-sqrt6` or `x=-1+sqrt6`