Question

How do you solve `x^2+4x+2=0`?

Answer 1

`x=-2+sqrt(2)`
or
`x=-2-sqrt(2)`

Explanation:

For any equation of the form
`color(white)("XXXX")` `ax^2+bx+c=0`
the solutions can be obtained using the quadratic formula:
`color(white)("XXXX")` `x= (-b+-sqrt(b^2-4ac))/(2a)`
(this formula shows up often enough that it is worth memorizing)

Substituting the values from `x^2+4x+2 = 0` for `a,b, and c`
`color(white)("XXXX")` `x= (-4+-sqrt(4^2-4(1)(2)))/(2(1))`

`color(white)("XXXX")` `x = (-4+-sqrt(8))/2`

`color(white)("XXXX")` `x=-2+-sqrt(2)`