Question

I figured out how to do this problem but I don't understand how it all worked out.. can someone please explain Kim wants to have equal amounts of room on all four sides of her dining room table. A 5ft by 8ft table is placed in the center of a rectangular room that has an area of 154 square feet. What is the width of the clear space Kim will have on all sides of her table?
answer: length of room =8+2x
width =5+2x
(8+2x)(5+2x)=154
40+10x+16x+4x^2=154
4x^2+26x-114=0
2x^2+13x-57=0
2x^2-6x+19x-57= 0
2x(x-3)+19(x-3)=0
(2x+19)(x-3)=0
x=-19/2 OR 3
x=3ft
I had someone help me but

Answer 1

I don't understand how they got numbers like 40+10x+16x... all that.. I don't get it

Answer 2

From (8+2x)(5+2x) . U foil this

Answer 3

so I would multiply it like 8*5 then 2*5 and 2*2?

Answer 4

Yea.
8*5 , 2x*5 , 8*2x , 2x*2x

Answer 5

Okay so length of the room=8+2x and width is 5+2x
(8+2x)(5+2x)=154
40+10x+16x+4^2=154
4x^2+26-114=0
then after that i'm confused because I don't understand why there's 114? is it because thats whats needed to make it 154?

Answer 6

So from the previous , they combined like terms. 10x+16x=26x
Then they subtracted 154 on both sides.
40-154=114. And on the right side 154-154=0

Answer 7

okay so it's just breaking it down basically? because then it goes on to being
2x^2+13x-57=0
2x^2-6x+19x-57=0
2x(x-3)+19(x-3)=0
(2x+19)(x-3)=0

Answer 8

The next step would be dividing everything by 2.
So u have 2x^2+13x-57
And then they broke up the middle term to-6x+19x
And then factored

Answer 9

I think I get it but idk they broke it down because 2 cant go into 13 right? so they made it 6 and it goes into 6 3 times and 19 if left because thats all you can do with it

Answer 10

@nikato

Answer 11

So they broke it up to 2x^2-6x+19x-5
And broke it down two terms at a time to factor

2x^2-6x=. 2x(x-3)
And
19x-57=. 19(x-3)
And because they both have (x-3)
U can write it as (x-3) time the outside which is (2x+19)
So
(x-3)(2x+19)

Answer 12

Okay I get it now thank you very much(:

Answer 13

Ur welcome