SOLUTION: I have to solve each problem then check my answer to be sure it is reasonable. Here's the problem: A ten-gallon aquarium holding African cichlids is 3 inches higher than it is w

Question 34925: I have to solve each problem then check my answer to be sure it is reasonable. Here's the problem:
A ten-gallon aquarium holding African cichlids is 3 inches higher than it is wide. It's length is 21 inches, and its volume is 2730 cubic inches. What are the height and width of the aquarium?
I have set it up to look like this:
(x-7)~2 + (x+1)~2 + x~2 then I have gotten that figured out to x~2-14x+49+x~2+2x+1=x~2 that is where I get stuck after subtracting the x~2 to get it on the same side as the rest of the equation.
Answer by mbarugel(146) (Show Source): You can put this solution on YOUR website!
Hello!
Let's call X to the width of the aquarium. We know that its height must be X+3. Also, its length is 21. Volume is calculated as width*height*length. So we get the following equation:

Now we can solve this quadratic equation using the standard procedure:

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=529 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 10, -13. Here's your graph:

As you can see the two solution are 10 and -13. We can disregard the -13 because width can't be negative. So we conclude that the width of the aquarium is 10 inches. Therefore, its height must be 13 inches.
You can check that

I hope this helps!
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