Algebra 2 question with polynomials

The area of a rug is given by : f(x) = -x(x-2) square feet. Explain why the area can't be 5 square feet. Please respond fast this is due in a couple of hours

I have no idea why anybody would express the area of a rug as negative x times something, but anyway, here goes:

-x(x - 2) = 5
-x² + 2x = 5
-x² + 2x - 5 = 0
x² - 2x + 5 = 0

When we try to solve this by the quadratic formula, the discriminant (number under the square root sign) is

(-2)² - 4 * 1 * 5 = 4 - 20 = -16

Since the square root of - 16 is not a real number, there is no real number solution. Assuming that x is supposed to represent some physical dimension, x would need to be a positive real number, and it's not.

The area of a rug is given by : f(x) = -x(x-2) square feet
See what would happen if the answer WAS 5
5 = -x(x-2)
5 = -x^2 + 2x
x^2 -2x + 5 = 0
We can't factor it, so we would use the quadratic equation: x =[ -b ± √(b^2-4ac)]/2a
In this case, lets just look at the determinant, b^2 - 4ac, which tells you how many solutions there should be
b^2 - 4ac = (-2)^2 - 4 * 5 * 1
= 4 - 20 = -18
We can't take the square root of a negative number, so there are no real solutions to this equation, and the rug can't be 5 square feet.

f(x)= -x² +2x
is a quadratic
parabola is open downward
max is x=1, y=1
that's why