Answer:
x = -14 and x = 12
Explanation:
Let x be the width of the rectangular room in feet. Then, according to the problem, the length of the room is 2 feet longer than the width, or x + 2 feet.
The area of a rectangle is given by the formula A = length × width, so we have:
A = (x + 2) × x = x^2 + 2x
We are also given that the area of the room is 168 square feet, so we set A = 168 and get:
x^2 + 2x = 168
This is a quadratic equation in standard form, where 1x^2 + 2x - 168 = 0. We can solve this equation by factoring or using the quadratic formula. This will give us the value(s) of x, which represents the width of the room. Once we have the width, we can find the length by adding 2 feet to it.
And x is : -14 and 12