Question

How do you solve using the completing the square method `x^2+ 8x + 2 = 0`?

Answer 1

`x=-4+-sqrt14`

Explanation:

`"to use the method of "color(blue)"completing the square"`

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

`"that is add " (8/2)^2=16" to both sides"`

`rArr(x^2+8xcolor(red)(+16))+2=0color(red)(+16)`

`rArr(x+4)^2+2=16`

`"subtract 2 from both sides"`

`(x+4)^2cancel(+2)cancel(-2)=16-2`

`rArr(x+4)^2=14`

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

`sqrt((x+4)^2)=+-sqrt14`

`rArrx+4=+-sqrt14`

`rArrx=-4+-sqrt14`