SOLUTION: {{{sqrt X+2 - sqrt X-3 = sqrt X-6}}} This is the problem I am trying to work out. I have tried foiling, quadratic equation, completing the square, but I am not coming up with a g

Algebra ->  Radicals -> SOLUTION: {{{sqrt X+2 - sqrt X-3 = sqrt X-6}}} This is the problem I am trying to work out. I have tried foiling, quadratic equation, completing the square, but I am not coming up with a g      Log On


   

Question 420909: sqrt+X%2B2+-+sqrt+X-3+=+sqrt+X-6
This is the problem I am trying to work out. I have tried foiling, quadratic equation, completing the square, but I am not coming up with a good answer. If you could help me I would appreciate it. I don't want to know the answer as much as how to do it.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt+%28X%2B2%29+-+sqrt+%28X-3%29+=+sqrt+%28X-6%29
;
square both sides
%28sqrt+%28X%2B2%29+-+sqrt+%28X-3%29%29%5E2+=+%28sqrt+%28X-6%29%29%5E2
:
FOIL the Left side
(x+2) - sqrt%28%28x%2B2%29%2A%28x-3%29%29+-+sqrt%28%28x%2B2%29%2A%28x-3%29%29 + (x-3) = (x-6)
:
Combine like terms, move the radical to right
x + x -x + 2 - 3 + 6 = 2sqrt%28%28x%2B2%29%2A%28x-3%29%29
;
FOIL inside the radical
x + 5 = 2sqrt%28x%5E2+-+x+-+6%29
:
square both sides
x^2 + 10x + 25 = 4(x^2 - x - 6)
x^2 + 10x + 25 = 4x^2 - 4x - 24
:
Combine like terms on the right
0 = 4x^2 - x^2 - 4x - 10x - 24 - 25
:
3x^2 - 14x - 49 = 0
Factors to
(3x + 7)(x - 7) = 0
positive solution is all want here
x = + 7
:
:
Check solution in the original equation
sqrt+%287%2B2%29+-+sqrt+%287-3%29+=+sqrt+%287-6%29
you can see that it checks out