So the equation is x^2 + 14x = -58 :: I did that and got -7 +/- 3i How would I check my answer?

A big part of math is pattern recognition. A lot of homework is just fighting with stuff so you will remember the pattern when you see it again. The most common pattern is (x + a) * (x + b) = x^2 + (a + b)x + ab and the special case (x + a) * (x - a) = x^2 - a^2. When you spot the pattern you can just write the answer from memory.

Now study this page until it seems obvious: en.wikipedia.org/wiki/Polynomial_remainder_theorem

x^2 + 14x = -58

x^2 + 14x + 58 = 0 So we want something of the form (x + a)(x + b) = 0. Factors of 58 are 2 & 29, and both are prime, so the roots have to be imaginary. Quadratic formula time. Check: www.wolframalpha.com/input/?i=solve+x%5E2+%2B+14x+%2B+58+%3D+0

Here is the plot and you can see that "imaginary roots" means the plot does not actually go to y=0 with real values of x.

www.wolframalpha.com/input/?i=plot+x%5E2+%2B+14x+%2B+58+%3D+0