## ParthKohli 2 years ago Solve \(x(x + 3) = -9\) NOT by the quadratic formula.

1. PeterPan

Well, clearly x cannot be positive, as that would mean x+3 is positive too. x must be negative, but no less than -3, or else x+3 would also be negative.

2. ParthKohli

Complex numbers?

3. ParthKohli

I know them by the quadratic formula

4. PeterPan

maybe?

5. PeterPan

Oh, right. I forgot to assume the real-ness of x... I'm lost :D

6. phi

you can complete the square as an alternative to the quadratric formula

7. PeterPan

That's kinda like using the quadratic formula anyway? :D

8. phi

you will get complex roots

9. ParthKohli

Well\[x^2 + 3x + 2.75 = -9 + 2.75\]

10. PeterPan

What's with the 2.75? You mean 2.25, right?

11. ParthKohli

Yes, whoops

12. sami-21

can i use compeleting square ??? or factor mehod ?

13. ParthKohli

\[(x + 1.5)^2 = -9 + 2.25\]Yes, I wanna know how to factor this over \(\mathbb C\) without knowing the roots!

14. PeterPan

It seems like it's already almost done?

15. sami-21

well, i guess this is a good condidate for completing square .

16. ParthKohli

OK, completing the square worked out well. Thanks @phi :-)