# How Do I Solve X=7+ Square Root Of 2x+1?

The square root of 2x + 1 can be written as (2x + 1)1/2 x = 7 + (2x + 1)1/2 square both sides
(x - 7)2 = ((2x + 1)1/2) 2 x2 -14x + 49 = 2x + 1
x2 -14x + 49 - 2x - 1 = 0
x2 - 16x + 48 = 0
factor
(x - 12)(x - 4) = 0
set each to 0 to determine the solution set
x - 12 = 0 x - 4 = 0
x = 12 x = 4
the answer is 4 and 12
the reason 4 works is because (2(4) + 1)1/2 = 91/2 = + 3 or -3
so 4 = 7 + (-3)
4 = 4
thanked the writer.
Jon McCarty commented
I see that after factoring we get 12 and 4. I get the 4, but I'm not seeing where the 12 fits into the original problem. Am I missing something?
Anonymous commented
Junior81,
substituting 12 back into the original equation:
X = 7 + (2x + 1)^1/2
12 = 7 + (2*12+1)^1/2
12 = 7 + (24+1)^1/2
12 = 7 + (25)^1/2
12 = 7 + 5
12 = 12
check complete
Jon McCarty commented
Jc61064,

That makes perfect sense. I was trying to put them both into the equation at the same time, that didn't work out so well. Now I see. Thank you.
Subtract 7 to the other side making it x-7
take the square root of both sides
and the problem should look like x squared -14x+49 = 2x+1
than just solve it
it would be x^2 -16x + 48 = 0
(x-12)(x-4)=0
x = 12 and 4
wow. Wasn't that easy? Maybe this will actually help in your further learning?
thanked the writer.
Jon McCarty commented
Thank you, I'm going to need lots of help in the next eight semesters of math ahead of me. I got help on the same problem from someone else, with the same results.

I understand that after factoring we get x = 12 and 4.
After I input the 4 back into the problem we get the square root of (2(4)+1) and that equals the square root of 9 or +3, -3. And 7 + (-3) = 4.

Where does the 12 fit in? 