Quick algebra question stuck in hw!!

x^2 + x + 1 = 0

i know the answer and is close to mine i did it like this but is wrong!!

x^2 +x = -1
(x + 1/2) ^ 2 = -1
x+1/2 = + or - squareroot of -1 or i

You forgot to actually complete the square ... take half middle coef and square it.Add to both sides.

x² + x + ¼ = –1 + ¼

(x + ½)² = –¾

Now when you take the square root of both sides you'll get ...

x + ½ = ± √(–3/4) = ±½√–3 = ±½i√3

So x = –½ ± ½√3 i

if you are solving by completing the square

x^2 + x = -1

x^2 + x + (1/2)^2 = -1 + (1/2)^2

x^2 + x + 1/4 = -1 + 1/4

(x + 1/2)(x + 1/2) = -3/4

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

x + 1/2 = ± √(-3/4)

x + 1/2 = ± i√3 / 2

x = (-1 ± i√3) / 2


quadratically
x^2 + x + 1 = 0
(-1 ± √-3) / 2
x = (-1 ± i√3) / 2