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) About Me  (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.


2x%2Bsqrt%28x%2B1%29=34


sqrt%28x%2B1%29=34-2x


%28sqrt%28x%2B1%29%29%5E2=%2834-2x%29%5E2 Square both sides (to eliminate the square root)


x%2B1=%2834-2x%29%5E2


x%2B1=%2834-2x%29%2834-2x%29


x%2B1=34%2834-2x%29-2x%2834-2x%29 Distribute


x%2B1=34%2834%29%2B34%28-2x%29-2x%2834%29-2x%28-2x%29 Distribute again


x%2B1=1156-68x-68x%2B4x%5E2


0=1156-68x-68x%2B4x%5E2-x-1


0=4x%5E2-137x%2B1155


4x%5E2-137x%2B1155=0


Now use the quadratic formula to get these two possible solutions


x+=+77%2F4 or x+=+15


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


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Let's test each possible solution


So let's first test x+=+77%2F4


2x%2Bsqrt%28x%2B1%29=34


2%2877%2F4%29%2Bsqrt%2877%2F4%2B1%29=34 Plug in x+=+77%2F4


43=34


That last equation above is false. This means x+=+77%2F4 is NOT a true solution. It needs to satisfy the original equation


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and let's test x+=+15


2x%2Bsqrt%28x%2B1%29=34


2%2815%29%2Bsqrt%2815%2B1%29=34 Plug in x+=+15


34=34


And that final equation is true. So x+=+15 is indeed a true solution.


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Final Answer:


The only solution is x+=+15

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