SOLUTION: Please help me solve this equation? {{{sqrt(5x-1)-1=sqrt(x+2)}}} I have tried: {{{(sqrt(5x-1)-1)^2=sqrt((x+2)^2)}}} {{{5x-1-2sqrt(5x-1)+1=x+2}}}

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Question 105233: Please help me solve this equation?

I have tried:

-5x+1 -1 = -5x
________________________

But from there I am stuck, the only thing I know is that x=2, but the teacher asks for the procedure...hope you can help me...thank you!!!

Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
Start with the given equation

Square both sides


Foil the left side


Subtract 5x from both sides


Combine like terms on both sides


Divide both sides by -2


Divide



Square both sides again (to get rid of the square root)


Foil the right side


Get all terms to one side


Combine like terms


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=4, b=-9, and c=2




Negate -9 to get 9




Square -9 to get 81 (note: remember when you square -9, you must square the negative as well. This is because .)




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 4 to get 8


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





Check:

However, we need to check if these solutions satisfy the original equation

Start with the given equation


Plug in


Simplify


Take the square root


Simplify. Since both sides are equal, the solution is verified


-------------------

Start with the given equation


Plug in


Simplify


Take the square root


Simplify. Since both sides are not equal, the solution is not really a solution. It is an extraneous solution


So our only solution is

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