Question

How do you solve using the completing the square method `x^2 +5x +4=0`?

Answer 1

`x=-4" or "x=-1`

Explanation:

`"To solve by "color(blue)"completing the square"`

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

`"that is " (5/2)^2=25/4`

`rArr(x^2+5xcolor(red)(+25/4))+4=0color(red)(+25/4)`

`rArr(x+5/2)^2+4=25/4`

`rArr(x+5/2)^2=25/4-4=9/4`

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

`sqrt((x+5/2)^2)=+-sqrt(9/4)`

`rArrx+5/2=+-3/2`

`rArrx=-5/2+-3/2`

`rArrx_1=-5/2-3/2=-4" and " x_2=-5/2+3/2=-1`