Question

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

Answer 1

`(1-sqrt6)` and `(1+sqrt6)`

Explanation:

To solve `x^2−2x−5=0` using the completing the square method, one picks up terms containing `x^2` and `x`. Here these are `x^2−2x`. Here coefficient of `x^2` is one and that of `x` is `-2`, hence adding half of the square of latter i.e. adding `(-1)^2` (i..e. `1`) should make `x^2−2x`, a complete square.

Hence for solving, let us add and subtract `1`, and doing this the equation becomes

`x^2−2x+1−6=0`

or `(x-1)^2-(sqrt6)^2=0`

i.e. `(x-1+sqrt6)(x-1-sqrt6)=0`

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