SOLUTION: 0=2x^2+7x-4

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Question 773274: 0=2x^2+7x-4
Answer by ramkikk66(644) About Me  (Show Source):
You can put this solution on YOUR website!
2%2Ax%5E2+%2B+7%2Ax+-+4+=+0 is a standard quadratic equation which we can solve 
through factorization.
Rewrite the equation, splitting 7x as 8x - x
2%2Ax%5E2+%2B+8%2Ax+-+x+-+4+=+0
2%2Ax%28x+%2B+4%29+-+1%28x+%2B+4%29+=+0
%282%2Ax+-+1%29%2A%28x+%2B+4%29+=+0
So the 2 roots are:
2%2Ax+-+1+=+0 or x+=+1%2F2
x+%2B+4+=+0 or x+=+-4
Hope you got it:)
See the graph below:


 
Solved by pluggable solver: SOLVE quadratic equation with variable


Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B7x%2B-4+=+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=%287%29%5E2-4%2A2%2A-4=81.
  
  Discriminant d=81 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-7%2B-sqrt%28+81+%29%29%2F2%5Ca.
  
    x%5B1%5D+=+%28-%287%29%2Bsqrt%28+81+%29%29%2F2%5C2+=+0.5
    x%5B2%5D+=+%28-%287%29-sqrt%28+81+%29%29%2F2%5C2+=+-4
    
    Quadratic expression 2x%5E2%2B7x%2B-4 can be factored:
  2x%5E2%2B7x%2B-4+=+2%28x-0.5%29%2A%28x--4%29
  Again, the answer is: 0.5, -4.
Here's your graph:

graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B7%2Ax%2B-4+%29