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

Question 172264: sqrt(x+7) - 2sqrt(x) = -2
Answer by Alan3354(69443) (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 (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=6400 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 9, 0.111111111111111. Here's your graph:

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

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