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

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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

Mathematics
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can you tell me what this length is? |dw:1442710140915:dw|
15?
no the 7 is the vertical dimension I'm asking for the total horizontal dimension
hint: |dw:1442710233263:dw|
30?
idk how you're getting that
do you see the stuff I circled?
yes
add them up to get ???
2x or x^2
x + 8 + x = ???
7
think of it like this `apple + apple = 2 apples` so `x + x = 2x` right?
yeah x8x?
so if x+x = 2x, then x+x+8 turns into what?
2x+8
good
|dw:1442710945434:dw|
so hopefully you see how that total length marked in the drawing is 2x+8 feet?
i finally do :D
ok great
what is this marked length here? |dw:1442711082155:dw|
2x+7?
good
|dw:1442711337192:dw|
now if the length was 2x+8 and the width was 2x+7, then what is the area of the rectangle?
4x+15?
you have to multiply (2x+8) with (2x+7) FOIL it out
could you show me ?
have you learned the box method? that's actually better than FOIL
4x^2+30x+56?
good, you used the box method to get that? or some other method?
box method
ok great
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
now get everything to one side
how
subtract 58 from both sides
|dw:1442712284053:dw|
|dw:1442712322065:dw|
|dw:1442712342649:dw|
4x^2+30x-2
correct
0 be left on the other side (since 58-58 = 0) so we have this answer `4x^2 + 30x - 2 = 0`
ok wow
tahnks alot for everything :)
no problem

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