1. Feb 16, 2012

### Tebow15

1. The problem statement, all variables and given/known data
-19x^2-20x-9=0

3. The attempt at a solution
With QF it looks like this:

x=20+-(sqrt):1084/-38

How would I factor this without the QF?

2. Feb 16, 2012

### Mentallic

No, that's not how it looks like. Check the discriminant (part under the square root) again.

This is one that doesn't have rational solutions so you can't factorize it in the usual sense that you're probably thinking. To factor trinomials like this, take a look at this video on how to do so:

But keep in mind that you can always factorize any quadratic if you know the quadratic formula. If a quadratic has roots a and b, then it can be factorized in the form (x-a)(x-b) so since you know the quadratic formula

$$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$

$$x_1=\frac{-b+\sqrt{b^2-4ac}}{2a}$$
$$x_2=\frac{-b-\sqrt{b^2-4ac}}{2a}$$
$$(x-x_1)(x-x_2)= \left(x-\frac{-b+\sqrt{b^2-4ac}}{2a}\right)\left(x-\frac{-b-\sqrt{b^2-4ac}}{2a}\right)$$