# How To Solve Problems With Imaginary Numbers

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.

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In this problem, that means that either (x - 9)^2 or (x^2 9) must be zero.

Now that we've split the equation up, we've got two smaller equations that we do know how to solve simply with inverse operations.

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Try it risk-free When you solve a quadratic equation with the quadratic formula and get a negative on the inside of the square root, what do you do?

The short answer is that you use an imaginary number.Getting the x by itself in this first one means undoing a power of 2 with a square root.The square root of zero is still just zero, so that leaves us here. Moving over to the other equation requires us to undo similar steps, just in a different order.If this is a new concept for you, then you should check out the previous lesson that introduces these ideas, but if you already know this, we're ready to look at the example 'find the roots of y = 2x^2 - 5x 7.' When a problem asks you for the roots, it is the same thing as asking for the zeros or the x-intercepts.These are the points where y = 0, so we can substitute that value in to begin with.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.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.We also have now taken the square root of a negative number, which means we have imaginary solutions as well!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.