The answer is rotation then translation. (:
Answer:
<em>The area of Marlien's living room is 420 square ft</em>
Step-by-step explanation:
Before calculating the real dimensions of Marlien's living room, we must find the value of x.
Given the total shape of the house is a rectangle, then both widths must be equal and both lengths must be equal.
The widths are already written width identical expressions x-2+x, but the lengths are given as different functions of x. Equating both expressions, we have:

Simplifying:
-10 + x - 2 = 2
x = 10 + 2 + 2
x = 14
Since x=14 feet, the dimensions of Marlien's living room are
width=x=14 feet
length=2x+2=30 feet
Thus the area is:
A = 14*30 = 420 square ft
The area of Marlien's living room is 420 square ft
Answer: x = (sqrt(7) + 2)/3 and
x = ( – sqrt(7) + 2)/3
Explanation:
3x^2 - 4x - 1 = 0
Divide both sides by 3:
3x^2/3 - 4/3x - 1/3 = 0/3
x^2 - 4/3x - 1/3 = 0
x^2 - 4/3x = 1/3
x^2 - 4/3x + (2/3)^2 = 1/3 + (2/3)^2
(x - 2/3)^2 = 1/3 + 4/9
(x - 2/3)^2 = 7/9
Sqrt both sides:
x - 2/3 = sqrt (7/9)
x - 2/3 = |sqrt(7)/3|
Set x -2/3 = sqrt(7)/3
=> x = (sqrt(7) + 2)/3
Set x - 2/3 = - sqrt(7)/3
=> x = ( - sqrt(7) + 2)/3