Question

How do you solve by completing the square: `x^2 + 4x + 2 = 0`?

Answer 1

x^2+4x+2=0#

Remove the `2` from the left side expression by subtracting `2` from both sides:
`x^2+4x=-2`

If the left side is to be a square its non-`x` term must be the coefficient of `x` divided by `2` then squared (i..e.`(4/2)^2 = 4`);
add this amount to both sides:
`x^2+4x+4=+2`

Rewrite the left-hand side as a square:
`(x+2)^2 = 2`

Take the square root of both sides
`x+2 = +-sqrt(2)`

Isolate `x` on the rights side (by subtracting `2` from both sides)
`x = -2+-sqrt(2)`

So the solutions are
`x=-2+sqrt(2)` and `x=-2-sqrt(2)`