SOLUTION: My wife and I are having a disagreement on the answer to this problem. Can you solve this in as much detail as possible please. Solve for x. I believe that x=9 and she is saying x=

Algebra ->  Radicals -> SOLUTION: My wife and I are having a disagreement on the answer to this problem. Can you solve this in as much detail as possible please. Solve for x. I believe that x=9 and she is saying x=      Log On


   

Question 924173: My wife and I are having a disagreement on the answer to this problem. Can you solve this in as much detail as possible please. Solve for x. I believe that x=9 and she is saying x=9,2
+++sqrt%28+X%2B7+%29+%2B5=X++
Found 3 solutions by ewatrrr, MathTherapy, Alan3354:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
+++sqrt%28+X%2B7+%29+%2B5=X++
+++sqrt%28+X%2B7+%29+=+X+-5%29++ Squaring Both Sides of the EQ
x + 7 = (x-5)^2
x + 7 = x^2 - 10x + 25
x^2 - 11x + 18 = 0
(x - 9)(x - 2) = 0
x = 2 , 9
whenever there is a √ or log involved, for ex., one needs to check to see if both solutions work

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
My wife and I are having a disagreement on the answer to this problem. Can you solve this in as much detail as possible please. Solve for x. I believe that x=9 and she is saying x=9,2
+++sqrt%28+X%2B7+%29+%2B5=X++ 


sqrt%28x+%2B+7%29+%2B+5+=+x

sqrt%28x+%2B+7%29+=+x+-+5 ------ Subtracting 5

%28sqrt%28x+%2B+7%29%29%5E2+=+%28x+-+5%29%5E2 ------- Squaring both sides

x+%2B+7+=+x%5E2+-+10x+%2B+25

x%5E2+-+10x+-+x+%2B+25+-+7+=+0

x%5E2+-+11x+%2B+18+=+0

(x - 9)(x - 2) = 0

x = 9          OR    x = 2

However, the ONLY solution is highlight_green%28x+=+9%29, since x = 2 is an EXTRANEOUS solution. 

AN EXTRANEOUS solution exists when a solution value is substituted back into the original equation and the original

equation PROVES FALSE. That's the case with x = 2, as when 2 is substituted for x, we get: 3 + 5 = 2, but 3+%2B+5%3C%3E+2



Hence, your wife is INCORRECT, and you're CORRECT, this TIME!!

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
If a man says something, and his wife is not there to hear it, is he still wrong?
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A recent study shows that women who "carry a few extra pounds" tend to live longer than the men who mention it.