SOLUTION: How to solve: 7b^2-14b-97=-8

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Question 860445: How to solve: 7b^2-14b-97=-8
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

7b^2-14b-97=-8

7b^2-14b-89=0

 


 
Solved by pluggable solver: SOLVE quadratic equation with variable


Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 7x%5E2%2B-14x%2B-89+=+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=%28-14%29%5E2-4%2A7%2A-89=2688.

  

  Discriminant d=2688 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--14%2B-sqrt%28+2688+%29%29%2F2%5Ca.

  

    x%5B1%5D+=+%28-%28-14%29%2Bsqrt%28+2688+%29%29%2F2%5C7+=+4.70328039909021

    x%5B2%5D+=+%28-%28-14%29-sqrt%28+2688+%29%29%2F2%5C7+=+-2.70328039909021

    

    Quadratic expression 7x%5E2%2B-14x%2B-89 can be factored:

  7x%5E2%2B-14x%2B-89+=+7%28x-4.70328039909021%29%2A%28x--2.70328039909021%29

  Again, the answer is: 4.70328039909021, -2.70328039909021.
Here's your graph:

graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+7%2Ax%5E2%2B-14%2Ax%2B-89+%29