Question

How do you solve `x^2 + x + 1=0` by completing the square?

Answer 1

This equation can't be solved by completing the square.
Since D = b^2 - 4ac = 1 - 4 = -3 < 0, there are complex roots.

Answer 2

In this way:

`x^2+x+1=0rArrx^2+x+1/4-1/4+1=0rArr`

`(x+1/2)^2=-1+1/4rArr(x+1/2)^2=-3/4`,

that is an impossible equation (no solutions) because a square can't be negative.