## help_people one year ago Tabitha wants to hang a painting in a gallery. The painting and frame must have an area of 58 square feet. The painting is 7 feet wide by 8 feet long. Which quadratic equation can be used to determine the thickness of the frame, x? Image of a frame 7 feet wide by 8 feet long, with an of x on the bottom and right sides x2 + 15x − 2 = 0 x2 + 15x + 58 = 0 4x2 + 30x − 2 = 0 4x2 + 30x + 58 = 0

1. help_people

@jim_thompson5910

2. jim_thompson5910

|dw:1442710030323:dw|

3. jim_thompson5910

|dw:1442710064925:dw|

4. jim_thompson5910

can you tell me what this length is? |dw:1442710140915:dw|

5. help_people

15?

6. jim_thompson5910

no the 7 is the vertical dimension I'm asking for the total horizontal dimension

7. jim_thompson5910

hint: |dw:1442710233263:dw|

8. help_people

30?

9. jim_thompson5910

idk how you're getting that

10. jim_thompson5910

do you see the stuff I circled?

11. help_people

yes

12. jim_thompson5910

add them up to get ???

13. help_people

2x or x^2

14. jim_thompson5910

x + 8 + x = ???

15. help_people

7

16. jim_thompson5910

think of it like this `apple + apple = 2 apples` so `x + x = 2x` right?

17. help_people

yeah x8x?

18. jim_thompson5910

so if x+x = 2x, then x+x+8 turns into what?

19. help_people

2x+8

20. jim_thompson5910

good

21. jim_thompson5910

|dw:1442710945434:dw|

22. jim_thompson5910

so hopefully you see how that total length marked in the drawing is 2x+8 feet?

23. help_people

i finally do :D

24. jim_thompson5910

ok great

25. jim_thompson5910

what is this marked length here? |dw:1442711082155:dw|

26. help_people

2x+7?

27. jim_thompson5910

good

28. jim_thompson5910

|dw:1442711337192:dw|

29. jim_thompson5910

now if the length was 2x+8 and the width was 2x+7, then what is the area of the rectangle?

30. help_people

4x+15?

31. jim_thompson5910

you have to multiply (2x+8) with (2x+7) FOIL it out

32. help_people

could you show me ?

33. jim_thompson5910

have you learned the box method? that's actually better than FOIL

34. help_people

4x^2+30x+56?

35. jim_thompson5910

good, you used the box method to get that? or some other method?

36. help_people

box method

37. jim_thompson5910

ok great

38. jim_thompson5910

so the entire area of the rectangle (larger rectangle) is `4x^2+30x+56` they tell us that "The painting and frame must have an area of 58 square feet." so equate the two areas 4x^2+30x+56 = 58

39. jim_thompson5910

now get everything to one side

40. help_people

how

41. jim_thompson5910

subtract 58 from both sides

42. jim_thompson5910

|dw:1442712284053:dw|

43. jim_thompson5910

|dw:1442712322065:dw|

44. jim_thompson5910

|dw:1442712342649:dw|

45. help_people

4x^2+30x-2

46. help_people

@jim_thompson5910

47. jim_thompson5910

correct

48. jim_thompson5910

0 be left on the other side (since 58-58 = 0) so we have this answer `4x^2 + 30x - 2 = 0`

49. help_people

ok wow

50. help_people

tahnks alot for everything :)

51. jim_thompson5910

no problem