Question

How do you solve using the completing the square method `x^2 = 2x + 4`?

Answer 1

`x = 3.236" "or" "x=-1.236`

Explanation:

In the equation `x^2 -2x-4=0`, `" "-4` is not `(b/2)^2`

`x^2 -2x " "=4" "larr`move `-4` to the right side

Add `color(blue)((b/2)^2)` to both sides `color(blue)( ((-2)/2)^2 =1)`

`x^2 -2x color(blue)(+1)=4color(blue)(+1)`

`" "(x-1)^2 =5`

`" "x-1 = +-sqrt5`

`" "x = +sqrt5+1color(white)(xxxxxx) or x = -sqrt5+1`

`" "x = +sqrt5+1color(white)(xxxxxx) or x = -sqrt5+1`

`x = 3.236" "or" "x=-1.236`