SOLUTION: square root of (x-5) - square root of (2x+7) = -3

Algebra ->  Algebra  -> Square-cubic-other-roots -> SOLUTION: square root of (x-5) - square root of (2x+7) = -3      Log On

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

   

Question 139847: square root of (x-5) - square root of (2x+7) = -3
Answer by ankor@dixie-net.com(12704) About Me  (Show Source):
You can put this solution on YOUR website!
square root of (x-5) - square root of (2x+7) = -3
:
sqrt%28x-5%29 - sqrt%282x%2B7%29 = -3
:
We can arrange this to get rid of the negatives and make it a little easier
sqrt%28x-5%29 + 3 = sqrt%282x%2B7%29
:
Square both sides (FOIL the left side)
[(x-5) + 6sqrt%28x-5%29 + 9] = 2x + 7
:
x + 6sqrt%28x-5%29 + 9 - 5 = 2x + 7
:
x + 6sqrt%28x-5%29 + 4 = 2x + 7
:
We want the radical by itself on the left:
6sqrt%28x-5%29 = 2x -x + 7 - 4
:
6sqrt%28x-5%29 = (x + 3)
:
Square both sides again (FOIL the right side)
36(x-5) = x^2 + 6x + 9
:
36x - 180 = x^2 + 6x + 9
:
combine like terms to obtain a quadratic equation
0 = x^2 + 6x - 36x + 9 + 180
:
x^2 - 30x + 189 = 0
Factor
(x-9)(x-21) = 0
Two solutions
x = 9
x = 21
:
Try both solutions in the original equation to make sure they are both valid