SOLUTION: I have an unsimplified equation and need to simplify it then solve for x: {{{( 3sqrt(2) - x )/( sqrt(x) ) = sqrt(2x)/ ( sqrt(2) - x ) }}} so if I simplify using cross multipl

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Question 976853: I have an unsimplified equation and need to simplify it then solve for x:

so if I simplify using cross multiply I should have?:


I'm new to doing this with square roots all involved, did I go about this right?
Found 2 solutions by josgarithmetic, Alan3354:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
I only partially checked your first step. Assuming your work is correct to the last equation shown, you now have a quadratic equation and can use general solution of a quadratic equation to solve for x.



-----you can simplify this yourself, and check if it is acceptable in the originally-given equation.


Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
I have an unsimplified equation and need to simplify it then solve for x:

so if I simplify using cross multiply I should have?:


I'm new to doing this with square roots all involved, did I go about this right?
================
Looks right. Solve for x.


Square both sides.


---
Sub u for x^2

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=1300 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 37.0277563773199, 0.972243622680054. Here's your graph:

================
x^2 = answers shown
Find the sq roots.
Check for extraneous solutions.


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