Subtractions such as 5 - 9 used to be impossible until negative numbers were invented, just as taking the square root of a negative number used to be impossible until imaginary numbers were invented. The square root of 9 is 3, but the square root of −9 is not −3. This is because −3 x −3 = +9, not −9. For a long time, it seemed as though there was no answer to the square root of −9.