SOLUTION: sqrt(x+7) - 2sqrt(x) = -2

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Question 172264: sqrt(x+7) - 2sqrt(x) = -2
Answer by Alan3354(21583) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt(x+7) - 2sqrt(x) = -2
sqrt(x+7) = 2sqrt(x) - 2
Square both sides
(x+7) = 4x -8sqrt(x) + 4
-3x + 3 = -8sqrt(x)
Square again
9x^2 - 18x + 9 = 64x
9x^2 + -82x + 9 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 9x%5E2%2B-82x%2B9+=+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=%28-82%29%5E2-4%2A9%2A9=6400.

Discriminant d=6400 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--82%2B-sqrt%28+6400+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-82%29%2Bsqrt%28+6400+%29%29%2F2%5C9+=+9
x%5B2%5D+=+%28-%28-82%29-sqrt%28+6400+%29%29%2F2%5C9+=+0.111111111111111

Quadratic expression 9x%5E2%2B-82x%2B9 can be factored:
9x%5E2%2B-82x%2B9+=+%28x-9%29%2A%28x-0.111111111111111%29
Again, the answer is: 9, 0.111111111111111. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+9%2Ax%5E2%2B-82%2Ax%2B9+%29

The factors are not correct, but the answers are.
x = 9
x = 1/9