Question

How do you solve by completing the square for `x^2+2x+6=0`?

Answer 1

y = x^2 + 2x + 6.

This quadratic equation doesn't have real roots. It has 2 complex roots.

Answer 2

`0 = x^2+2x+6 = x^2+2x+1+5 = (x+1)^2+5`

Subtracting 5 from both sides we get

`(x+1)^2 = -5`

The square of any real number is positive or zero, so this has no solutions for real values of `x`.