SOLUTION: I asked this problem earlier, but have learned how to type it so that it is easier for you to read and understand. I need to square this problem. Problem: 2x^2+4x-1=0 Formula I u

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: I asked this problem earlier, but have learned how to type it so that it is easier for you to read and understand. I need to square this problem. Problem: 2x^2+4x-1=0 Formula I u      Log On


   

Question 288295: I asked this problem earlier, but have learned how to type it so that it is easier for you to read and understand. I need to square this problem.
Problem: 2x^2+4x-1=0
Formula I used was: %28-4%2B-sqrt%284%5E2-4%2A2%2A-1%29%29%2F%282%2A2%29
I got:
%28-4%2B-sqrt%2816-4%2A2%2A-1%29%29%2F%282%2A2%29
then %28-4%2B-sqrt%2816%2B8%29%29%2F%282%2A2%29
then %28-4%2B-sqrt%2824%29%29%2F%282%2A2%29
then %28-4%2B-2sqrt%286%29%29%2F%282%2A2%29 (this is supposed to read "+ or - 2" not -2)
then %28-4%2B-2sqrt%286%29%29%2F%284%29 (this is supposed to read "+ or - 2", not -2)
then after simplifying, I get
%28-1%2B-sqrt%286%29%29%2F%282%29
My book says the answer is: %28-2%2B-sqrt%286%29%29%2F%282%29
I can't figure out where I went wrong, so I can't answer my real question of 2x^2+10x-3=0.
Any help is appreciated!! Thank you!
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
then %28-4%2B-2sqrt%286%29%29%2F%284%29 (this is supposed to read "+ or - 2", not -2)
then after simplifying, I get
%28-1%2B-sqrt%286%29%29%2F%282%29 **** This last step is not right ***
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My book says the answer is: %28-2%2B-sqrt%286%29%29%2F%282%29
I can't figure out where I went wrong, so I can't answer my real question of 2x^2+10x-3=0.
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2x^2+10x-3=0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B10x%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=%2810%29%5E2-4%2A2%2A-3=124.

Discriminant d=124 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-10%2B-sqrt%28+124+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2810%29%2Bsqrt%28+124+%29%29%2F2%5C2+=+0.283882181415011
x%5B2%5D+=+%28-%2810%29-sqrt%28+124+%29%29%2F2%5C2+=+-5.28388218141501

Quadratic expression 2x%5E2%2B10x%2B-3 can be factored:
2x%5E2%2B10x%2B-3+=+%28x-0.283882181415011%29%2A%28x--5.28388218141501%29
Again, the answer is: 0.283882181415011, -5.28388218141501. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B10%2Ax%2B-3+%29

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= (-5 ± sqrt(31))/2