SOLUTION: Solve √(2x+3) - √(2x)=1

Algebra ->  Algebra  -> Radicals -> SOLUTION: Solve √(2x+3) - √(2x)=1      Log On

Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!
Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

   

Question 178168: Solve √(2x+3) - √(2x)=1
Found 2 solutions by stanbon, Mathtut:
Answer by stanbon(48535) About Me  (Show Source):
You can put this solution on YOUR website!
Solve √(2x+3) - √(2x)=1
Square both sides to get:
2x+3 -2sqrt(2x(2x+3) - 2x = 1
Combine:
-2sqrt(4x^2+6x) = -2
sqrt(4x^2+6x) = 1
Square both sides to get:
4x^2 + 6x = 1
Rearrange:
4x^2 + 6x -1 = 0
Use quadratic formula:
x = [-6 +- sqrt(36 - 4*4*-1] / 8
x = [-6 +- sqrt(52)/8
x = [-6 +- 2sqrt(13)]/8
x = [3 +- sqrt(13)]/4
============================
Check the answers to see if any are extraneous.
===============================================
Cheers,
Stan H.

Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%282x%2B3%29-sqrt%282x%29=1
:
sqrt%282x%2B3%29=1%2Bsqrt%282x%29added sqrt of 2x from both sides
:
2x%2B3=%281%2Bsqrt%282x%29%29%5E2squaring both sides...
:
2x%2B3=1%2B2sqrt%282x%29%2B2xmultiplied out right side
:
2=2sqrt%282x%29isolated sqrt on right and combined like terms on left
:
1=sqrt%282x%29divided by 2
:
1=2xsquared both sides
:
highlight%28x=1%2F2%29divided both sides by 2 to isolate variable x