SOLUTION: Hello! I have tried working this problem but when I checked my answer it did not work with the problem. Here is the problem: Solve the following equations algebraically:

Algebra ->  Radicals -> SOLUTION: Hello! I have tried working this problem but when I checked my answer it did not work with the problem. Here is the problem: Solve the following equations algebraically:       Log On


   

Question 95525: Hello!
I have tried working this problem but when I checked my answer it did not work with the problem. Here is the problem:
Solve the following equations algebraically:
sqrt(2x+3)-sqrt(x+7)=1
Here is my work:
I squared both sides to give me
2x+3-x+7=1
Next I added like terms to get x+10=1
I brought over the 1 to give me x=9
I must be doing something wrong. Any help will be appreicated.



Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt(2x+3)-sqrt(x+7)=1
Square both sides to get:
(2x+3) - 2sqrt[(2x+3)(x+7)] +(x+7) = 1
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Simplify:
(3x+10) - 2sqrt[.....] = 1
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Isolate the sqrt term:
-2sqrt[.....} = 1-3x-10
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Simplify:
-2sqrt[..........] = -(3x+9)
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Square both sides to get:
4(2x+3)(x+7) = 9x^2+54x+81
4(2x^2+17x+21) = 9x^2+54x+81
8x^2+68x+84 = 9x^2+54x+81
x^2-14x-3=0
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Use the quadratic formula:
x = [14+-sqrt(14^2-4*-3)]/2
x = [14 +- 14.42]/2
x = 14.21... or x = -0.2111...
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These answers need to be checked in the original equation as
one or both may be extraneous.
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Cheers,
Stan H.