SOLUTION: Solve for x by factoring. x^2 + 2x - 1= 0

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Question 482025: Solve for x by factoring. x^2 + 2x - 1= 0
Answer by jorel1380(3719) About Me  (Show Source):
You can put this solution on YOUR website!
x^2 + 2x - 1=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B2x%2B-1+=+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=%282%29%5E2-4%2A1%2A-1=8.

Discriminant d=8 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-2%2B-sqrt%28+8+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%282%29%2Bsqrt%28+8+%29%29%2F2%5C1+=+0.414213562373095
x%5B2%5D+=+%28-%282%29-sqrt%28+8+%29%29%2F2%5C1+=+-2.41421356237309

Quadratic expression 1x%5E2%2B2x%2B-1 can be factored:
1x%5E2%2B2x%2B-1+=+1%28x-0.414213562373095%29%2A%28x--2.41421356237309%29
Again, the answer is: 0.414213562373095, -2.41421356237309. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B2%2Ax%2B-1+%29