SOLUTION: I cannot solve the following, please help and show step by step if possible, thank you {{{matrix(1,3,sqrt(7x+29), "=", x+3)}}}

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Question 176651This question is from textbook Elementary and Intermediate Algebra
: I cannot solve the following, please help and show step by step if possible, thank you
This question is from textbook Elementary and Intermediate Algebra

Found 2 solutions by jim_thompson5910, Edwin McCravy:
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
Start with the given equation.


Square both sides


FOIL


Subtract 7x from both sides. Subtract 29 from both sides.


Combine like terms.


Factor the right side



Now set each factor equal to zero:

or


or Now solve for x in each case


So the possible answers are or


However, if you plug in , you'll find that the original equation will not be true. So is NOT a solution


==========================================================

Answer:

So the only solution is

Answer by Edwin McCravy(20055)   (Show Source): You can put this solution on YOUR website!
I cannot solve the following, please help and show step by step if possible, thank you


Since the radical is already isolated on the left,
square both sides.









Get 0 on the left by subtracting  from
both sides:



or



Factor left side:



Use the principle of zero factors:

  

But we have to check each of those,
because squaring both sides, or multiplying
both sides by a variable, may result in
bogus solutiona, called "extraneous"
solutions.

Checking 







That checks, so  is a solution.

Checking 







That does not check, so  is not 
a solution, and is called "extraneous".

The only genuine solution is 

Edwin

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