SOLUTION: The length of a rectangle is 3 units less than 6 times its width. The area of the rectangle is 145 square units. Which of the following equations can be used to find w, the width o

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: The length of a rectangle is 3 units less than 6 times its width. The area of the rectangle is 145 square units. Which of the following equations can be used to find w, the width o      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 922428: The length of a rectangle is 3 units less than 6 times its width. The area of the rectangle is 145 square units. Which of the following equations can be used to find w, the width of the rectangle?
A. 7w - 3 = 145
B. 6w^2 - 18w = 145
C. 7w - 18 = 145
D. 6w^2 - 3w = 145
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

     .

A = Lw

(6w-3)w = 145

6w^2 -3w = 145

.........

6w^2 - 3w - 145 = 0

 


 
Solved by pluggable solver: SOLVE quadratic equation with variable


Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 6x%5E2%2B-3x%2B-145+=+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=%28-3%29%5E2-4%2A6%2A-145=3489.

  

  Discriminant d=3489 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--3%2B-sqrt%28+3489+%29%29%2F2%5Ca.

  

    x%5B1%5D+=+%28-%28-3%29%2Bsqrt%28+3489+%29%29%2F2%5C6+=+5.17231314187412

    x%5B2%5D+=+%28-%28-3%29-sqrt%28+3489+%29%29%2F2%5C6+=+-4.67231314187412

    

    Quadratic expression 6x%5E2%2B-3x%2B-145 can be factored:

  6x%5E2%2B-3x%2B-145+=+6%28x-5.17231314187412%29%2A%28x--4.67231314187412%29

  Again, the answer is: 5.17231314187412, -4.67231314187412.
Here's your graph:

graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+6%2Ax%5E2%2B-3%2Ax%2B-145+%29