So i need finding the area of the living room. the question says it’s got to be at least 140 feet. but i can’t find a number for x that fits the equation.

Given: parameter=142feet
A(area) of living room=140ft^2

First, find x
Parameter=142ft=2x((2x-10)+(x-2)+(x-2)+(1/2x-4))+2x((x-2)+(x))

142=2x(9/2x-18)+2x(2x-2)
142=9x-36+4c-4
142=13x-40
182=13x
14=x

Area of the living room(A)=140=(x)x(2x+2)
A=140=(14)x(2(14)+2)
A=140=14 x 30
A=140=420ft^2

The area must not be 140ft^2 or the parameter is not 142

It is noticeable that the calculated area of the living room is 3 times as large as the given

Another method

Given area of the living room=140
Area=width x length

140=(x) x (2x+2)

140=2x^2+2x

0=2x^2+2x-140

0=x^2+x-70

0=ax^2+bx+c

x=(-b+/-(b^2-4ac)^1/2)/2a

x=(-1+/-(1^2-4(1)(-70))^1/2)/2(1)

x=(-1+/-(1+280)^1/2)/2

x=-1+/-(16.763)/2

x=-1+8.3815 or -1-8.315

x=7.3815 or -9.3815

Because width can only be positive, so c=7.3815

Plug in to test

140=(7.3815) x (2(7.3815)+2)
140=(7.3815) x (14.763+2)
140=7.3815 x 16.763
140=131.000
This solution does not work

x=9.3815

140=(-9.3815) x (2(-7.3815)+2)
140=(-9.3715) x (-14.763+2)
140=(-9.3715) x (-12.763)
140=138.499

Ok, I guess the width of the living room is negative

Something’s wrong