SOLUTION: How does n=4 in the problem: sqrt(n)+6=sqrt(16n)? Please show me

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Question 603653: How does n=4 in the problem: sqrt(n)+6=sqrt(16n)? Please show me
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
How does n=4 in the problem: sqrt(n)+6=sqrt(16n)?
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sqrt%28n%29%2B6=sqrt%2816n%29
sqrt%284%29%2B6=sqrt%2816%2A4%29
2%2B6=sqrt%2864%29
8 = 8
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sqrt(n)+6=sqrt(16n)
Square both sides
n + 12sqrt(n) + 36 = 16n
12sqrt(n) = 15n - 36
Square again
144n = 225n^2 - 1080n + 1296
25n^2 - 136n + 144 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 25x%5E2%2B-136x%2B144+=+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=%28-136%29%5E2-4%2A25%2A144=4096.

Discriminant d=4096 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--136%2B-sqrt%28+4096+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-136%29%2Bsqrt%28+4096+%29%29%2F2%5C25+=+4
x%5B2%5D+=+%28-%28-136%29-sqrt%28+4096+%29%29%2F2%5C25+=+1.44

Quadratic expression 25x%5E2%2B-136x%2B144 can be factored:
25x%5E2%2B-136x%2B144+=+%28x-4%29%2A%28x-1.44%29
Again, the answer is: 4, 1.44. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+25%2Ax%5E2%2B-136%2Ax%2B144+%29