SOLUTION: Solve the following equations algebraically. Approximate the result to 3 decimal places. In x + in(x+1)=1

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Question 480432: Solve the following equations algebraically. Approximate the result to 3 decimal places.
In x + in(x+1)=1
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
I think you mean natural logs.
ln(x) + ln(x+1) = 1
ln%28x%2A%28x%2B1%29%29+=+1
ln%28x%5E2+%2B+x%29+=+1
x%5E2+%2B+x+=+e
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B1x%2B-2.71828182845905+=+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=%281%29%5E2-4%2A1%2A-2.71828182845905=11.8731273138362.

Discriminant d=11.8731273138362 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-1%2B-sqrt%28+11.8731273138362+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%281%29%2Bsqrt%28+11.8731273138362+%29%29%2F2%5C1+=+1.22287022972105
x%5B2%5D+=+%28-%281%29-sqrt%28+11.8731273138362+%29%29%2F2%5C1+=+-2.22287022972105

Quadratic expression 1x%5E2%2B1x%2B-2.71828182845905 can be factored:
1x%5E2%2B1x%2B-2.71828182845905+=+%28x-1.22287022972105%29%2A%28x--2.22287022972105%29
Again, the answer is: 1.22287022972105, -2.22287022972105. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B1%2Ax%2B-2.71828182845905+%29