SOLUTION: Solve the following equation using the Quadratic Formula. 2x²-11x-2=0 The solution set is { } Type an exact answer, using radicals as needed. Use a comma to separate answers as

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Solve the following equation using the Quadratic Formula. 2x²-11x-2=0 The solution set is { } Type an exact answer, using radicals as needed. Use a comma to separate answers as       Log On


   

Question 241498: Solve the following equation using the Quadratic Formula.
2x²-11x-2=0
The solution set is { }
Type an exact answer, using radicals as needed. Use a comma to separate answers as needed.

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
2x²-11x-2=0
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Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B-11x%2B-2+=+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=%28-11%29%5E2-4%2A2%2A-2=137.

Discriminant d=137 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--11%2B-sqrt%28+137+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-11%29%2Bsqrt%28+137+%29%29%2F2%5C2+=+5.67617497767991
x%5B2%5D+=+%28-%28-11%29-sqrt%28+137+%29%29%2F2%5C2+=+-0.176174977679906

Quadratic expression 2x%5E2%2B-11x%2B-2 can be factored:
2x%5E2%2B-11x%2B-2+=+%28x-5.67617497767991%29%2A%28x--0.176174977679906%29
Again, the answer is: 5.67617497767991, -0.176174977679906. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-11%2Ax%2B-2+%29

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= (11/4) ±sqrt(137)/4