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.
s ʌ b t ɹ æ k ʃ ə n z WORD_BOUNDARY s ʌ t̠ʃ WORD_BOUNDARY ʌ z WORD_BOUNDARY f aɪ v WORD_BOUNDARY n aɪ n WORD_BOUNDARY j uː z d WORD_BOUNDARY t ə b i WORD_BOUNDARY ɪ m p ɑ s ɪ b ə l WORD_BOUNDARY ʌ n t ɪ l WORD_BOUNDARY n ɛ ɡ ə t ɪ v WORD_BOUNDARY n ʌ m b ə ɹ z WORD_BOUNDARY w ɜː ɹ WORD_BOUNDARY ɪ n v ɛ n t ɪ d WORD_BOUNDARY d̠ʒ ʌ s t WORD_BOUNDARY æ z WORD_BOUNDARY t eɪ k ɪ ŋ WORD_BOUNDARY ð ə WORD_BOUNDARY s k w ɛ ɹ WORD_BOUNDARY ɹ uː t WORD_BOUNDARY ə v ə WORD_BOUNDARY n ɛ ɡ ə t ɪ v WORD_BOUNDARY n ʌ m b ə ɹ WORD_BOUNDARY j uː z d WORD_BOUNDARY t ə b i WORD_BOUNDARY ɪ m p ɑ s ɪ b ə l WORD_BOUNDARY ʌ n t ɪ l WORD_BOUNDARY ɪ m æ d̠ʒ ɪ n ɛ ɹ i WORD_BOUNDARY n ʌ m b ə ɹ z WORD_BOUNDARY w ɜː ɹ WORD_BOUNDARY ɪ n v ɛ n t ɪ d WORD_BOUNDARY ð ə WORD_BOUNDARY s k w ɛ ɹ WORD_BOUNDARY ɹ uː t WORD_BOUNDARY ʌ v WORD_BOUNDARY n aɪ n WORD_BOUNDARY ɪ z WORD_BOUNDARY θ ɹ iː WORD_BOUNDARY b ʌ t WORD_BOUNDARY ð ə WORD_BOUNDARY s k w ɛ ɹ WORD_BOUNDARY ɹ uː t WORD_BOUNDARY ʌ v WORD_BOUNDARY m aɪ n ə s WORD_BOUNDARY n aɪ n WORD_BOUNDARY ɪ z WORD_BOUNDARY n ɑ t WORD_BOUNDARY m aɪ n ə s WORD_BOUNDARY θ ɹ iː WORD_BOUNDARY ð ɪ s WORD_BOUNDARY ɪ z WORD_BOUNDARY b ɪ k ʌ z WORD_BOUNDARY m aɪ n ə s WORD_BOUNDARY θ ɹ iː WORD_BOUNDARY ɛ k s WORD_BOUNDARY m aɪ n ə s WORD_BOUNDARY θ ɹ iː WORD_BOUNDARY iː k w ə l z WORD_BOUNDARY p l ʌ s WORD_BOUNDARY n aɪ n WORD_BOUNDARY n ɑ t WORD_BOUNDARY m aɪ n ə s WORD_BOUNDARY n aɪ n WORD_BOUNDARY f ə ɹ ɹ ə WORD_BOUNDARY l ɔ ŋ WORD_BOUNDARY t aɪ m WORD_BOUNDARY ɪ t WORD_BOUNDARY s iː m d WORD_BOUNDARY æ z WORD_BOUNDARY ð oʊ WORD_BOUNDARY ð ɛ ɹ w ʌ z WORD_BOUNDARY n oʊ WORD_BOUNDARY æ n s ə ɹ WORD_BOUNDARY t ə WORD_BOUNDARY ð ə WORD_BOUNDARY s k w ɛ ɹ WORD_BOUNDARY ɹ uː t WORD_BOUNDARY ʌ v WORD_BOUNDARY m aɪ n ə s WORD_BOUNDARY n aɪ n WORD_BOUNDARY