SOLUTION: How to solve for x in the equation log(sub 5)(x+4) + log(sub 5)(x) = 2

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Question 114690: How to solve for x in the equation
log(sub 5)(x+4) + log(sub 5)(x) = 2
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
log(5)(x+4)+log(5)x=2
log(5)(x(x+4))=2
log(5)(x^2+4x)=2
x^2+4x=5^2
x^2+4x-25=0
x=3.38516... Quadratic formula (see below)
Ed
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B4x%2B-25+=+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=%284%29%5E2-4%2A1%2A-25=116.

Discriminant d=116 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-4%2B-sqrt%28+116+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%284%29%2Bsqrt%28+116+%29%29%2F2%5C1+=+3.3851648071345
x%5B2%5D+=+%28-%284%29-sqrt%28+116+%29%29%2F2%5C1+=+-7.3851648071345

Quadratic expression 1x%5E2%2B4x%2B-25 can be factored:
1x%5E2%2B4x%2B-25+=+%28x-3.3851648071345%29%2A%28x--7.3851648071345%29
Again, the answer is: 3.3851648071345, -7.3851648071345. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B4%2Ax%2B-25+%29