SOLUTION: Solve the following equation: 11y^2 +2y -1 = 0

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Question 985926: Solve the following equation:
11y^2 +2y -1 = 0
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
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Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ay%5E2%2Bby%2Bc=0 (in our case 11y%5E2%2B2y%2B-1+=+0) has the following solutons:

y%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%2A11%2A-1=48.

Discriminant d=48 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-2%2B-sqrt%28+48+%29%29%2F2%5Ca.

y%5B1%5D+=+%28-%282%29%2Bsqrt%28+48+%29%29%2F2%5C11+=+0.224009237739796
y%5B2%5D+=+%28-%282%29-sqrt%28+48+%29%29%2F2%5C11+=+-0.405827419557978

Quadratic expression 11y%5E2%2B2y%2B-1 can be factored:
11y%5E2%2B2y%2B-1+=+11%28y-0.224009237739796%29%2A%28y--0.405827419557978%29
Again, the answer is: 0.224009237739796, -0.405827419557978. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+11%2Ax%5E2%2B2%2Ax%2B-1+%29

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ANSWER: y=0.224 or y=-0.406