Question

Solve \(x(x + 3) = -9\) NOT by the quadratic formula.

Answer 1

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.

Answer 2

Complex numbers?

Answer 3

I know them by the quadratic formula

Answer 4

maybe?

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

you will get complex roots

Answer 9

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

Answer 10

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

Answer 11

Yes, whoops

Answer 12

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

Answer 13

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

Answer 14

It seems like it's already almost done?

Answer 15

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

Answer 16

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