SOLUTION: lnx + ln (x+3) = 1

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Question 386020: lnx + ln (x+3) = 1
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
lnx + ln (x+3) = 1
ln x(x+3) = 1
x(x+3) = e^1
x^2+3x = e^1
x^2+3x-e = 0
x^2+3x-2.7183 = 0
Applying the "quadratic formula" we get:
x= {0.728968371242625, -3.72896837124262}
Throw out the negative solution (extraneous) which leaves us with:
x = 0.729
.
Details of quadratic to follow:
.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B3x%2B-2.7183+=+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=%283%29%5E2-4%2A1%2A-2.7183=19.8732.

Discriminant d=19.8732 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-3%2B-sqrt%28+19.8732+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%283%29%2Bsqrt%28+19.8732+%29%29%2F2%5C1+=+0.728968371242625
x%5B2%5D+=+%28-%283%29-sqrt%28+19.8732+%29%29%2F2%5C1+=+-3.72896837124262

Quadratic expression 1x%5E2%2B3x%2B-2.7183 can be factored:
1x%5E2%2B3x%2B-2.7183+=+1%28x-0.728968371242625%29%2A%28x--3.72896837124262%29
Again, the answer is: 0.728968371242625, -3.72896837124262. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B3%2Ax%2B-2.7183+%29