## kdarnell08 2 years ago 4x^2+81-36x

1. tkcena75

(2x-9)^2

2. kdarnell08

can ya go through the steps for me?

3. tcarroll010

There are a couple of ways to do this. The quickest is factoring, if you are good at seeing factors. This is a little tricky with factoring, so when in doubt you can always use the quadratic formula (the second way) which is actually my favorite way.$x = \frac{ -b \pm \sqrt{b ^{2} - 4ac} }{ 2a }$where you have an equation in the form: ax^2 + bx + c = 0 So you have a=4, b=-36, and c=81 So, you substitute those into the formula.

4. kdarnell08

ughh i just dont understand this!!

5. tcarroll010

Well, let's look at factoring for a bit instead. As for factoring (the other way), you can rewrite the equation into: (2x)^2 - 36x + 9^2 You will see that the first term is a square and the third term is a square which might sugeest that the factors are squared.

6. tcarroll010

That means that we can partially set up the solution: (2x )(2x ) But the third term is a square also, so going a bit further and just leaving out the signs: (2x 9)(2x 9) Now this all presupposes you can work the distributive law well enough: (a + b)(c + d) = a(c + d) + b(c + d) = ac + ad + bc + bd Tell me before we go any further, can you deal with that last equation?

7. kdarnell08

yes.

8. tcarroll010

That's great! That really is. Don't worry if it's a little rocky. You're not supposed to "see it all" right away, so we'll just go along until it gets murky for you. np. So, continuing where we left off with the factoring, writing it again: (2x 9)(2x 9) We have a good start, but we don't have signs yet. We know that 81 is positive so the signs are both negative or both positive. Since the 36x has a negative sign, we go with negative signs: (2x - 9)(2x - 9)

9. tcarroll010

Now, we are goingto multiply this out to check our work: (2x)(2x - 9) - 9(2x - 9) = 4x^2 - 18x - 18x + 81 = 4x^2 - 36x + 81

10. tcarroll010

So, that's the same as our original expression with a slight change in order of the terms. So, that's 2 ways to do this. Ok, your turn, ask questions.

11. kdarnell08

ok. i understand most of it i just dont understand what happened to the #36

12. tcarroll010

In the checking of the solution that I did, the -36x came from the -18x -18x

13. kdarnell08

i get it!!!!!

14. tcarroll010

Believe me. If really get this or most of it, or even half. That's real progress! For anyone! I suggest going over this a couple times to consolidate your understanding

15. tcarroll010

And don't give up on the quadratic formula because that is actually much more important.

16. kdarnell08

ok i already copied and pasted it to a word document. and ive used the equations for more than one of the other problems i have!

17. tcarroll010

You very nice to work with because you really want to learn (all students should be that way) and you are a nice person.

18. kdarnell08

thank you! i appreciate that. maybe its because they are mostly in high school. im in nursing school and am relearning everything and harly remember it all. i personallt DO NOT want to have to repay for this class. hs was 5 years ago so its a little more than rocky.

19. kdarnell08

and its an online class. which is way harder than on campus

20. tcarroll010

This is good what you just said. You are approaching this from a perspective that is more mature than high school. And the world needs good nurses. My sister is a nurse. She was also a math whiz, so she breezed through math. But just get through math since you already have a higher goal. And good luck in both math but especially the nursing!

21. kdarnell08

thank you!

22. tcarroll010

You are entirely welcome!

23. kdarnell08

did i mention i hate rational expressions :)

24. tcarroll010

lol then go with the irrational ones :-)

25. tcarroll010

A little math humor. There's so little material from which to get humor in math!

26. kdarnell08

haha. oh i am aware!

27. tcarroll010

I think the developers of all these math formulas are secretly laughing in their graves at all the misery they caused!

28. tcarroll010

I know! Maybe one day you can get a math PhD. as a patient! Payback!

29. kdarnell08

hahahahaha. thats funny!!! i wouldnt doubt it!! all i know is this is the only subject that i curl up in the fetal position and cry over ;)

30. tcarroll010

Math is tough because it is so unforgiving and as a field of study, it is so vertical. Can't go too far ahead without getting the basics.

31. kdarnell08

uh oh. got to another one....wanna help?

32. tcarroll010

vertical as in concepts building upon one another. Sure, I've got time for one more. Then I curl up and cry.

33. kdarnell08

$\frac{ x ^{2}-25 }{ x+5 }$

34. tcarroll010

Oh, you'll like this one because it's easier than the other one.

35. kdarnell08

oh god i hope so lol

36. kdarnell08

dont you get rid of the division and turn it to multipication

37. tcarroll010

Sort of. I'm going to factor the numerator:$\frac{ (x + 5) \times (x - 5) }{ (x + 5) }$Now, the division concept comes into play insofar as the x + 5 factor cancels out of the numerator and the denominator and you are left with: x - 5 as your answer.

38. kdarnell08

that i comletely understand!

39. tcarroll010

Either the website or my computer just went goofy.