SOLUTION: solve for x lnx + ln(x+7)=2

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Question 637682: solve for x
lnx + ln(x+7)=2
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
solve for x
lnx + ln(x+7)=2
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Adding logs --> multiplying
ln(x*(x+7)) = 2
x%2A%28x%2B7%29+=+e%5E2
x%5E2+%2B+7x+-+e%5E2+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B7x%2B7.38905609893065+=+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=%287%29%5E2-4%2A1%2A7.38905609893065=19.4437756042774.

Discriminant d=19.4437756042774 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-7%2B-sqrt%28+19.4437756042774+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%287%29%2Bsqrt%28+19.4437756042774+%29%29%2F2%5C1+=+-1.29524516077879
x%5B2%5D+=+%28-%287%29-sqrt%28+19.4437756042774+%29%29%2F2%5C1+=+-5.70475483922121

Quadratic expression 1x%5E2%2B7x%2B7.38905609893065 can be factored:
1x%5E2%2B7x%2B7.38905609893065+=+%28x--1.29524516077879%29%2A%28x--5.70475483922121%29
Again, the answer is: -1.29524516077879, -5.70475483922121. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B7%2Ax%2B7.38905609893065+%29

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x = (-7/2) ± sqrt(49 + 4e^2)/2
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e and e^2 are just constants.