SOLUTION: solve 2r^2 + 3r-1=0 answer: -3 + sqrt 17/4, -3-sqrt 17/4 need a full break down of how my text book got this answer

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Question 193384: solve 2r^2 + 3r-1=0

answer: -3 + sqrt 17/4, -3-sqrt 17/4
need a full break down of how my text book got this answer
Answer by yuendatlo(23) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ar%5E2%2Bbr%2Bc=0 (in our case 2r%5E2%2B3r%2B-1+=+0) has the following solutons:

r%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=%283%29%5E2-4%2A2%2A-1=17.

Discriminant d=17 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-3%2B-sqrt%28+17+%29%29%2F2%5Ca.

r%5B1%5D+=+%28-%283%29%2Bsqrt%28+17+%29%29%2F2%5C2+=+0.280776406404415
r%5B2%5D+=+%28-%283%29-sqrt%28+17+%29%29%2F2%5C2+=+-1.78077640640442

Quadratic expression 2r%5E2%2B3r%2B-1 can be factored:
2r%5E2%2B3r%2B-1+=+2%28r-0.280776406404415%29%2A%28r--1.78077640640442%29
Again, the answer is: 0.280776406404415, -1.78077640640442. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B3%2Ax%2B-1+%29
sorry about the weird decimals