SOLUTION: Find all real solutions of the equation. Enter DNE in any empty blank. 2x + √(x + 1)= 34 x = x = Please explain Thank you

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Question 932211: Find all real solutions of the equation. Enter DNE in any empty blank.
2x + √(x + 1)= 34
x =
x =
Please explain
Thank you
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
The idea is to isolate the square root and then square both sides. From there you solve for x.








Square both sides (to eliminate the square root)








Distribute


Distribute again














Now use the quadratic formula to get these two possible solutions


or


Let me know if you need to see the steps to the quadratic formula (I skipped those steps to save space).


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


Let's test each possible solution


So let's first test





Plug in





That last equation above is false. This means is NOT a true solution. It needs to satisfy the original equation


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


and let's test





Plug in





And that final equation is true. So is indeed a true solution.


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


Final Answer:


The only solution is

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