Can someone tell me whether this can be solved by factoring, completing the square, or using the quadratic formula. y=-x^2+10x-19

Question

kainui · Answer

I don't think you'll be able to solve it by factoring, but you can always complete the square or use the quadratic formula. The quadratic formula is actually the "equation" version of completing the square.

hero · Answer

It can be solved by factoring.

hero · Answer

So it can be solved using all three methods.

hero · Answer

@AshleyBananas, Why did you give me the medal  ?

anonymous · Answer

because you answered my question

anonymous · Answer

@Hero

hero · Answer

Did you solve it by factoring yet?

hero · Answer

@AshleyBananas, are you factoring it?

anonymous · Answer

@Hero you can't solve by factoring?

hero · Answer

Do you want me to post the steps for you?

hero · Answer

@AshleyBananas

anonymous · Answer

THANK YOU SO MUCH THAT WOULD BE GREAT! I don't understand this.

anonymous · Answer

@Hero

hero · Answer

I'll post the solution hang on a bit

hero · Answer

$$
\-x^2 + 10x -19
\-(x^2 - 10x + 19)
\-(x^2 +(5 + \sqrt{6})x +(5 - \sqrt{6})x - 19)
\ -(x(x + 5 + \sqrt{6}) + (5 - \sqrt{6})(x + 5 +\sqrt{6})
\-(x + 5 - \sqrt{6})(x + 5 + \sqrt{6})
$$

anonymous · Answer

@Hero thank you so much I really appreciate it

hero · Answer

You're welcome

kainui · Answer

That's exactly how I factored in middle school.

hero · Answer

By the way, we figure it out like this:

$$10 = (5 + \sqrt{6} - \sqrt{6} + 5)$$
$$19 = (5 + \sqrt{6})(5 - \sqrt{6})$$

hero · Answer

Doesn't matter. Every quadratic can be factored. The question, in my opinion, is a silly one.

kainui · Answer

Obviously every one can be factored, but I think you should take into consideration the context of the course. It would seem to be implied that this means "factored into whole numbers".

anonymous · Answer

My teacher taught us that not every equation can be factored @Hero and @Kainui she does not care if they are whole numbers or not.

kainui · Answer

...

hero · Answer

I think you mean "assumptions" @Kainui. @AshleyBananas, your teacher is wrong. All you have to do is show her your work from what I posted. She may even be baffled by it.

kainui · Answer

lol ok whatever.