How do I solve x^2+2x+4>0 and what does the solution tell you?
let's look at x^2 + 2x + 4 = 0
by completing the square, (in this case the easiest way to solve it)
x^2 + 2x = -4
x^2 + 2x + 1 = -4+1
(x+1)^2 = -3
but anything squared cannot be negative, so there is no real solution
consider y = x^2 + 2x + 4
this parabola never touches or crosses the a-axis, and since it opens upwards, must lie totally above the x-axis.
so x^2 + 2x+4 > 0 is true for all values of x