SOLUTION: hELLO, I NEED A QUADRATIC FORMULA FOR A RECTANGLE WHO'S AREA IS 100 METERS. I KNOW THAT AREA = LENGTH * WIDTH AND MY RECTANGLE'S WIDTH IS 2 TWO TIMES THE LENGTH + 3 METERS. I JUST

Question 489412: hELLO, I NEED A QUADRATIC FORMULA FOR A RECTANGLE WHO'S AREA IS 100 METERS. I KNOW THAT AREA = LENGTH * WIDTH AND MY RECTANGLE'S WIDTH IS 2 TWO TIMES THE LENGTH + 3 METERS. I JUST NEED HELP SETTING UP THE PROPER FUNCTION FOR THIS PROBLEM PLEASE.I NEED TO ELIMINATE ONE OF THE VARIABLES BUT I AM CONFUSED WHERE TO START.
Answer by jorel1380(3719) (Show Source): You can put this solution on YOUR website!
l(2l+3)=100
2l^2+3l-100=0

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=809 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 6.36073132666395, -7.86073132666395. Here's your graph:

Throwing out the negative answer, we get the rectangle's length to be 6.36073132666395 meters..
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