Question 135617
I see nothing wrong with what you have done and your answer is correct.
When you say that it is not a "complete" quadratic equation, what you mean is that in the general form:{{{ax^2+bx+c = 0}}} , b happens to be zero but that doesn't mean that you don't have a quadratic equation.
The proof, of course, is to solve your answer to see if you get the given solutions of: x = 3i and x = -3i

{{{x^2+9 = 0}}} Subtract 9 from both sides.
{{{x^2 = -9}}} Take the square root of both sides.
{{{x = sqrt(-9)}}} or {{{x = -sqrt(-9)}}} and {{{sqrt(-9) = 3sqrt(-1)}}} = {{{3i}}} so...
{{{x = 3i}}} or {{{x = -3i}}}