SOLUTION: Solve √(3x+1)= 7- √(x-4)

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Question 176937: Solve √(3x+1)= 7- √(x-4)
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Solve sqrt%283x%2B1%29 = 7+-+sqrt%28x-4%29
square both sides, you have to foil the right side
3x + 1 = 49 - 14sqrt%28x-4%29 + (x-4)
:
3x + 1 = 49 - 14sqrt%28x-4%29 + x - 4
:
3x + 1 = x + 45 - 14sqrt%28x-4%29
;
3x - x + 1 - 45 = 14sqrt%28x-4%29
:
2x - 44 = - 14sqrt%28x-4%29
square both sides, FOIL the left side, remove the radical on the right
4x^2 - 176x + 1936 = 196(x-4)
;
4x^2 - 176x + 1936 = 196x - 784
:
4x^2 - 176x -196x + 1936 + 784 = 0
:
4x^2 - 372x + 2720 = 0
Simplify divide by 4
x^2 - 93x + 680 = 0
Factors to
(x-8)(x-85) = 0
two solutions
x = 8
x = 85
:
Check both solutions in the original equation, only one is valid