SOLUTION: c) Solve the equation 2x² + 2x – 3 = 0

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Question 841550: c) Solve the equation 2x² + 2x – 3 = 0
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

2x² + 2x – 3 = 0

 


 
Solved by pluggable solver: SOLVE quadratic equation with variable


Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B2x%2B-3+=+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=%282%29%5E2-4%2A2%2A-3=28.

  

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

  

    x%5B1%5D+=+%28-%282%29%2Bsqrt%28+28+%29%29%2F2%5C2+=+0.822875655532295

    x%5B2%5D+=+%28-%282%29-sqrt%28+28+%29%29%2F2%5C2+=+-1.8228756555323

    

    Quadratic expression 2x%5E2%2B2x%2B-3 can be factored:

  2x%5E2%2B2x%2B-3+=+2%28x-0.822875655532295%29%2A%28x--1.8228756555323%29

  Again, the answer is: 0.822875655532295, -1.8228756555323.
Here's your graph:

graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B2%2Ax%2B-3+%29