That trinomial can't be factored. You would have to complete the square to factor it and even then your answer would be an imaginary number.
x² + x + 12 = 0
x² + x = - 12
x² + x + 1/4 = - 12 + 1/4
x² + x + 1/4 = - 11 3/4
x² + x + 1/4 = - 47/4
(x + 1/2)² = - 47/4
x + 1/2 = +/- √(- 47/4)
x + 1/2 = +/- [tex] \frac{47}{4}i [/tex]
x = 1/2 +/- [tex] \frac{47}{4}i [/tex]
If the constant was a negative, it would be factor-able (is that a word?).
