Question

Solve:
2x^2+12x+9=0

So far I can't get any numbers that multiply to be 18 and add to be 12...

Answer 1

There aren't any two such numbers.
That's a good observation on your part.
That means you need to use the quadratic formula since the trinomial cannot be factored.

Answer 2

Thanks, is there an informal rule that is loosely used to tell people that if you can't factor an equation, use the quadratic formula?

Answer 3

Yes. A great question.
Use the discriminant of the quadratic formula:

\( b^2 - 4ac\)

You can only factor the trinomial if the discriminant is a perfect square.

Let's l;ook at your problem.
\(b^2 - 4ac\) for a = 2, b =- 12, c = 9 gives us:

\(12^2 - 4(2)(9) \)

\(= 144 - 72\)

\(= 72\)

72 is not a perfect square. Its square root simplifies to:

\( 3\sqrt{2} \)