Question

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

Answer 1

Solution: `x = (-4 +3 sqrt 2) ,x= ( -4 - 3sqrt 2)`

Explanation:

`x^2+8 x-2=0 or x^2+8 x=2` or

`x^2+8 x +16 =2+16` or

`(x+4)^2= 18 or (x+4) = +- sqrt 18` or

`x+4 = +- 3sqrt 2 or x = -4+- 3 sqrt 2`

Solution: `x = (-4 +3 sqrt 2) ,x= ( -4 - 3sqrt 2)`[Ans]

Answer 2

Take the second coefficient, divide it by 2, and square it, to complete the square, and obtain the solutions:
`x=-4+sqrt18` and `x=-4-sqrt18`

Explanation:

To complete the square, take the second coefficient (the one next to the `x`), divide it by 2, and square it. This will give you the number you need to complete the square.
In this case, that would be `(8-:2)^2 = 16`

Add this number to both sides of the original equation:
`(x^2+8x+16) - 2 = 16`
`(x+4)^2 - 2 = 16`
`(x+4)^2 = 18`

This gives us 2 possible solutions:
`x+4 = +-sqrt18`

`x=-4+-sqrt18`

Answer 3

`x=-4+-3sqrt2`

Explanation:

`"add 2 to both sides"`

`x^2+8x=2`

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

`x^2+2(4)x color(red)(+16)=2color(red)(+16)`

`(x+4)^2=18`

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

`sqrt((x+4)^2)=+-sqrt18larrcolor(blue)"note plus or minus"`

`x+4=+-sqrt18=+-sqrt(9xx2)=+-3sqrt2`

`"subtract 4 from both sides"`

`x=-4+-3sqrt2larrcolor(red)"exact values"`

`x~~-8.24" or "x~~0.24" to 2 dec. places"`