Each solution to x^2 + 5x + 18 = 0 can be written in the form a + bi where a and b are real numbers. What is a^2 + b^2?
+1633 Instead of doing the entire problem by getting each root exactly, why not try and use Vieta's formula to get ab and a + b instead?
ab = 18 and a + b = -5. Thus, a^2 + b^2 = (a + b)^2 - 2ab. Then a^2 + b^2 = 25 - 36.
Thus, a^2 + b^2 = -11. 
+1633 Oh yes! Thank you for your input everyone! But I caught a quick error! The solution ITSELF is a + bi, the solutions AREN'T a, and b. Thus, we might have to use the quadratic formula to find the solutions.
Applying the quadratic formula x=−b±√b2−4ac2a. We get -5 +- sqrt(25 - 72) / 2.
Thus the two solutions are −52+√−472 and −52−√−472.
In this case, it doesn't matter whether b is negative or positive since we are squaring it eventually. a is 5/2. Thus, a^2 = 25/4 and b^2 = -47 or -188/4.
That means, a2+b2=−1634, which approximates to -40.75.
