SOLUTION: 7-sqrt(1-4x)-sqrt(4-6x)=0 I have no idea how to do this problem. Please help!

Question 836280: 7-sqrt(1-4x)-sqrt(4-6x)=0
I have no idea how to do this problem. Please help!
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
This is a long and messy problem. The basic idea is this though: Isolate the square roots one by one on their own side. That will allow you to square both sides to eliminate each square root one by one. After doing all that, you can use the quadratic formula to solve for x. Remember to check ALL possible answers.

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Now use the quadratic formula to solve for x

Solved by pluggable solver: Quadratic Formula

Let's use the quadratic formula to solve for x:

Starting with the general quadratic

the general solution using the quadratic equation is:

So lets solve ( notice , , and )

Plug in a=1, b=242, and c=480

Square 242 to get 58564

Multiply to get

Combine like terms in the radicand (everything under the square root)

Simplify the square root (note: If you need help with simplifying the square root, check out this solver)

Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

or

Lets look at the first part:

Add the terms in the numerator

Divide

So one answer is

Now lets look at the second part:

Subtract the terms in the numerator

Divide

So another answer is

So our solutions are:

or

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So the *possible* solutions are or

However, we must check them both

Checking

This is TRUE, so is definitely a solution.

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Checking

This is FALSE, so is NOT a solution.

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Final Answer:
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