SOLUTION: [SQRT(x + 7)] - 2[SQRT(x)] =-2 I know x = 9 but I am not sure how to get there. How tall is a stack of cube-shaped blocks whose volumes are 375 cubic inches, 648 cubic inches

Question 168292: [SQRT(x + 7)] - 2[SQRT(x)] =-2
I know x = 9
but I am not sure how to get there.
How tall is a stack of cube-shaped blocks whose volumes are 375 cubic inches, 648 cubic inches and 1,029 cubic inches?
A. 10 cubert(3)
B. 6 cubert(3)
C. 3 sqrt(3)
D. 4 sqrt(3)
E. 9 sqt(3)
F. 18 cubert(3)
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
[SQRT(x + 7)] - 2[SQRT(x)] =-2
I know x = 9
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The simplest way is to get one radical by itself, then square both sides.
[SQRT(x + 7)] - 2[SQRT(x)] =-2

Now square

Now isolate the other radical

Square again

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 onsite solver doesn't do factors correctly if the coefficient of the the x^2 is not 1, but the answers are right, 9 and 1/9.
---------------------------------------
How tall is a stack of cube-shaped blocks whose volumes are 375 cubic inches, 648 cubic inches and 1,029 cubic inches?
A. 10 cubert(3)
B. 6 cubert(3)
C. 3 sqrt(3)
D. 4 sqrt(3)
E. 9 sqt(3)
F. 18 cubert(3)
-------------------
I don't know what you mean by that. More info is needed.
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