Equation: x^2-5x+6=0

It was a while ago, but I need to get back at it again so here is my sheet.

Using what is called PQ-formula in Swedish (x^2+px+q=0)

So here is what I got

p=-5
q=6

x=5/2 +- sq root of (5/2^2) -6

x= 2.5 +- 2.5^2 -6

x= 2.5 +- 6.25 - 6

x= 2.5 +- .25

x1 = 2.75
x2 = 2.25

BUT the answer is supposted to somehow be:

x1= 2
x2= 3

Please someone highlight where I went wrong and show me how I can fix it. It's really been a while and I feel like I lost everything

Idk what a pq switch is but it looks like you attempted to use the quadratic formula. This is fine but you are forgetting parts of it in the numerator we should have

-b +- sqrt(b^2 -4ac)


It would appear you’re missing parts of this.

Go to mathisfun and look at their quadratic formula example as a guide

Ok I think I got it now, please make sure I did it right

x^2-5x+6=0
x=5+-sqrt 5^2-4*1*6/2*1 (used the Quadratic Formula from here: https://www.mathsisfun.com/algebra/quadratic-equation.html)

x=5+-1/2

x1 = 3
x2 = 2

wohoo surely that's how it works right?

Brings me to my next problem which is:

I know that to solve "v" out of s=v*t I need to isolate v on the right side of the equation first so I remove t from there by dividing v*t/t and doing the same on the left side s/t
That leaves me with s/t=v

So v= s/t

But what about this one:

Solve V out of p=m/v?, it's supposed to be V=m/p but I can't figure out how to do it when it's put like that

Yeah just watch the order of operations

Common mistakes occur when trying to divide before using the square root

As for the pq switch thing I believe you are confusing factoring and the quadratic formula. I used to teach out of a textbook that had something similar to the p q switch you were talking about.

But I solved it correctly in this post right?

Yeah I'm going to be more careful moving on and really take my time on it to not do wrong!

I was confusing factoring and quadratic formula, my excuse is that it's been a while but I'm trying my best to get back to it

S=vt

We see multiplication before the v and the t. You undid this operation by dividing (this is inverse operations).

P=m/v

We see m being divided by v. We need to undo division so we use the inverse operation to multiply both sides by v

P*v= (m/v)*v

P*v=mv/v

P*v=m


Now we see multiplication between the p and the v. We need to use the inverse operation and divide both sides by p.

(P*v)/p=m/p

V=m/p

I was just pointing out that eventually you will be asked to write the quadratic in factored form. That’s when you can think pq switch. Factoring will be immensely more useful down the road. Factor whenever possible.

It seemed right in your post.

Thanks a lot!
I will probably do some more posts here whenever I feel like it's needed. Sorry if you feel it is too easy, gotta start somewhere I guess

Post when you have questions. Someone will answer.