What are the roots of 4x^2 + 176 = 0?

Roots are the same as zeros, and you find them by factoring and solving for y.  This one is easiest if done by "taking roots" method.  Let's move the 176 over to the other side and then divide both sides by 4 to get the x^2 alone.  If we do that have we get x^2 = -44.  But we know that we cannot take the square root of a negative number without accounting for it by using the imaginary "i".  Since "i" is equal to -1, let's rewrite that [sqrt-44] as [sqrt(-1)(44)].  Now let's simplify the 44 by finding its perfect square hidden in there: [sqrt(-1)(4)(11)].  Now, because -1 = i^2, we can rewrite that as well like this:
[sqrt(i^2)(4)(11)].  Both the i^2 and the 4 are perfect squares so that's what we pull out, leaving the 11 inside for an answer of x = +/- 2i[sqrt(11)]