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

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> 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       Log On


   

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) About Me  (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 ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B3x%2B-100+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%283%29%5E2-4%2A2%2A-100=809.

Discriminant d=809 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-3%2B-sqrt%28+809+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%283%29%2Bsqrt%28+809+%29%29%2F2%5C2+=+6.36073132666395
x%5B2%5D+=+%28-%283%29-sqrt%28+809+%29%29%2F2%5C2+=+-7.86073132666395

Quadratic expression 2x%5E2%2B3x%2B-100 can be factored:
2x%5E2%2B3x%2B-100+=+2%28x-6.36073132666395%29%2A%28x--7.86073132666395%29
Again, the answer is: 6.36073132666395, -7.86073132666395. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B3%2Ax%2B-100+%29

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