SOLUTION: Can somebody help me with these series of questions? Thank you so much. I appreciate it a lot. Alexa 28. a. Write an expression for the total area of the model below. htt

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: Can somebody help me with these series of questions? Thank you so much. I appreciate it a lot. Alexa 28. a. Write an expression for the total area of the model below. htt      Log On


   

Question 436247: Can somebody help me with these series of questions?
Thank you so much. I appreciate it a lot.
Alexa
28. a. Write an expression for the total area of the model below.
http://i1202.photobucket.com/albums/bb364/Small-Beatle/sa029-1.jpg
b. The total area is 110 m2. Write an equation to find x.
c. Solve the equation by completing the square. (4 points)
Answer by jorel1380(3719) About Me  (Show Source):
You can put this solution on YOUR website!
The total area is given by LXW, which is a.(x+2)(2x+2).
b. (x+2)(2x+2)=110
2x2+6x-106=0
x2+3x-53=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B3x%2B-53+=+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%2A1%2A-53=221.

Discriminant d=221 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-3%2B-sqrt%28+221+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%283%29%2Bsqrt%28+221+%29%29%2F2%5C1+=+5.93303437365925
x%5B2%5D+=+%28-%283%29-sqrt%28+221+%29%29%2F2%5C1+=+-8.93303437365925

Quadratic expression 1x%5E2%2B3x%2B-53 can be factored:
1x%5E2%2B3x%2B-53+=+1%28x-5.93303437365925%29%2A%28x--8.93303437365925%29
Again, the answer is: 5.93303437365925, -8.93303437365925. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B3%2Ax%2B-53+%29

Throwing out the negative value, we get x=5.933034.