Question

How do you solve using the completing the square method `x^2+4x-1=0`?

Answer 1

`x=-2+-sqrt5`

Explanation:

`"to "color(blue)"complete the square"`

add `(1/2" coefficient of x-term")^2" to both sides"`

`"that is add " 1/2(4/2)^2=4" to both sides"`

`x^2+4x+color(red)(4)-1=0+color(red)(4)`

`rArr(x+2)^2-1=4`

`"add 1 to both sides"`

`rArr(x+2)^2=5`

`color(blue)"take the square root of both sides"`

`rArrx+2=+-sqrt5larr" note plus or minus"`

`rArrx=-2+-sqrt5`

Answer 2

`x=-2+-sqrt5`

Explanation:

`x^2+4x-1=0`
`x^2+4x+(4/2)^2-(4/2)^2-1=0`
`(x+2)^2-5=0`
`(x+2)^2=5`
`x=-2+-sqrt5`