You cannot factor it, and it has no real roots!!. However, it has "complex roots" as follows:
Solve for x:
x^2 + 3 x + 4 = 0
Subtract 4 from both sides:
x^2 + 3 x = -4
Add 9/4 to both sides:
x^2 + 3 x + 9/4 = -7/4
Write the left hand side as a square:
(x + 3/2)^2 = -7/4
Take the square root of both sides:
x + 3/2 = (i sqrt(7))/2 or x + 3/2 = -(i sqrt(7))/2
Subtract 3/2 from both sides:
x = (0 + i/2) sqrt(7) - 3/2 or x + 3/2 = -(i sqrt(7))/2
Subtract 3/2 from both sides:
Answer: |x = (0 + i/2) sqrt(7) - 3/2 or x = (0 - i/2) sqrt(7) - 3/2
