When we take the square root of a non-zero number, we need to include the positive and negative root, giving us two answers here.
As long as you keep this in mind and don't think that complex numbers require you to do anything really radical, you should be good.
To review: the discriminant (b^2 - 4ac) will tell you whether you have real or complex solutions to a quadratic equation in standard form.
That means putting an i in front of the square root and continuing on like normal, just like before.
This time we can go further because the square root of 9 is just 3.
The most outside thing here is the 9, so we have to undo that first.
That leaves us with x^2 = -9, and then again we take the square root of both sides to get the x by itself.
For the longer, more helpful answer, check out this lesson!
By allowing ourselves to imagine that square roots of negative numbers actually exist, we are able to solve a lot of real-world problems. How would you go about solving a problem that has an imaginary solution? You'll need to remember that imaginary numbers come about when we take the square root of a negative number, and complex numbers are when we combine a real number with an imaginary one using addition or subtraction.
When you need to take the square root of a negative number, just put an i in front of it, make the number on the inside positive and continue on like normal.
You can solve higher-order polynomial problems using the zero product property, which says that when you multiply two things together and get zero, one of the things you started with must have been zero.