Question 522256
He has 30m of fencing materials and wants the corral to have an area of 100m^2. What are the dimensions of the corral?
Let x =width and y = length
2x+y=30
Change to a form we can use for substitution 
y = (30-2x)
:
The area
 x * y = 100
replace y with (30-2x)
x(30-2x) = 100
-2x^2 + 30x - 100 = 0; a quadratic equation
simplify and change the sign to make it easier to factor, divide by -2
x^2 - 15x + 50 = 0
Factors to 
(x-10)(x-5) = 0
two solutions
x = 5 meters, then y = 20 meters is the length (5*20=100)
x = 10 meters, then  y = 10 meters is the length (10*10=100)
:
Check both these solutions to ensure 30 m of fencing is used