## calculusxy one year ago MEDAL!!! What values of m satisfies the equation m^2 - 5m = 36 ? A. -1 and 5 B. 2 and -3 C. 4 and -1 D. 6 and -6 E. 9 and -4

1. calculusxy

$m^2 - 5m = 36$

2. anonymous

Sub and chug

3. anonymous

subtract 5m from both sides

4. hartnn

start by subtracting 36 from both sides, then it'll come in the form of $$ax^2+bx+c = 0$$

5. anonymous

its E.

6. calculusxy

I still don't understand @hartnn

7. anonymous

e) 9,-4

8. hartnn

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9. calculusxy

Okay

10. hartnn

now there are several methods to solve it. lets use the easiest one, splitting the middle term can you think of 2 numbers whose sum is -5 but product is -36?

11. hartnn

hint : one of the number is positive

12. calculusxy

Well I can find 9 and -4 but if I add them, it is 5 not -5.

13. hartnn

right so change the signs of both the numbers and try :)

14. calculusxy

So that would be -9 and 4 right?

15. hartnn

correct! :) so we split our middle term -5m as -9m + 4m

16. anonymous

its 9 and -4

17. hartnn

$$m^2 -9m+4m -36 = 0$$ lets consider 1st 2 terms only m^2 -9m what do you see common from both these terms?

18. calculusxy

The variables are the same.

19. hartnn

Hi Ana, we really appreciate you helping the asker by giving them the answer, but this site is primarily for the purpose of learning which can be done only by interactions, like we are doing right now :)

20. hartnn

so, "m" is common right? can you factor out m from m^2-9m ?

21. calculusxy

I am not sure :\

22. hartnn

$$\large ☻☺+☻♥= ☻(☺+♥) \\ \text{this is factoring, } \\ \text{☻ was common from both terms and factored out.}$$

23. hartnn

$$m^2 -9m = m\times m - 9\times m = m \times (m-9)$$ see if this makes sense :)

24. calculusxy

Yes :)

25. hartnn

cool, so lets test how much have you understood :P what is common from +4m -36 ?? factor that out!

26. calculusxy

4 and if you factor that out, then we can have $4 \times m - (4 \times 9) = 4(m - 9)$

27. hartnn

excellent! so now we have $$m (m-9) +4 (m-9) = 0$$ what is common from 1st 2 terms!?? factor that out!

28. calculusxy

I don't understand what you mean

29. hartnn

$$\large ☻☺+☻♥= ☻(☺+♥) \\ \text{this is factoring, } \\ \text{☻ was common from both terms and factored out.}$$ $$\large m(m-9) + 4(m-9) =0\\ \text {(m-9) is common from both therms!} \\ \Large (m-9)(m+4) =0$$

30. calculusxy

Oh yes !

31. hartnn

so now we use the fact that if ab =0 a= 0 or b=0

32. hartnn

(m-9)(m+4) = 0 then ?

33. calculusxy

Would that mean that m = 0?

34. hartnn

(m-9)(m+4) = 0 means either one of (m-9) or (m+4) has to be 0, so that product becomes 0 means m-9 =0 OR m+4 = 0 makes sense?

35. calculusxy

Yes.

36. hartnn

m-9 = 0 what does m equal ?? m+4 = 0 what does m equal ??

37. calculusxy

m-9=0 m = 9 m+4 = 0 m = -4

38. hartnn

$$\huge \checkmark$$

39. calculusxy

Oh!!! Thank you so much!!! I get how it is 9 and -4 thank you!

40. calculusxy

I have another question.

41. hartnn

welcome ^_^ happy learning :)

42. hartnn

43. calculusxy

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44. calculusxy

In the figure about, point A is the center of the circle and a vertex of the right triangle, which has an area of 12 square units and where angle BAC is the right. Point D (not shown) is the point of intersection of the perimeter of circle A and segment An. The ratio of Ab to AC is 2 to 3 and the ratio of AD and AB is 1 to 2. What is the area of the shaded region, in square units?

45. calculusxy

@hartnn