SOLUTION: Use the quadratic Formula to solve this equation. Round to the nearest tenth. Show your work.: A rectangular courtyard covers 20ft squared. The courtyard is 3 ft longer than it is

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Use the quadratic Formula to solve this equation. Round to the nearest tenth. Show your work.: A rectangular courtyard covers 20ft squared. The courtyard is 3 ft longer than it is      Log On


   

Question 310359: Use the quadratic Formula to solve this equation. Round to the nearest tenth. Show your work.:
A rectangular courtyard covers 20ft squared. The courtyard is 3 ft longer than it is wide. Find the dimensions of the courtyard.
Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
LW=20
L=3%2BW
%283%2BW%29W=20
W%5E2%2B3W=20
W%5E2%2B3W-20=0 view below.
W=3.2169905660283 has to be positive
L=3%2BW
L=3%2B3.2169905660283
L=6.2169905660283
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation aW%5E2%2BbW%2Bc=0 (in our case 1W%5E2%2B3W%2B-20+=+0) has the following solutons:

W%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%2A1%2A-20=89.

Discriminant d=89 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-3%2B-sqrt%28+89+%29%29%2F2%5Ca.

W%5B1%5D+=+%28-%283%29%2Bsqrt%28+89+%29%29%2F2%5C1+=+3.2169905660283
W%5B2%5D+=+%28-%283%29-sqrt%28+89+%29%29%2F2%5C1+=+-6.2169905660283

Quadratic expression 1W%5E2%2B3W%2B-20 can be factored:
1W%5E2%2B3W%2B-20+=+1%28W-3.2169905660283%29%2A%28W--6.2169905660283%29
Again, the answer is: 3.2169905660283, -6.2169905660283. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B3%2Ax%2B-20+%29