SOLUTION: \sqrt{x}+ 4 = 2\sqrt{x+5} solve and check

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Question 164396: \sqrt{x}+ 4 = 2\sqrt{x+5} solve and check
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%28x%29%2B+4+=+2%2Asqrt%28x%2B5%29
%28sqrt%28x%29%2B+4%29%5E2+=+%282%2Asqrt%28x%2B5%29%29%5E2
x%2B8%2Asqrt%28x%29%2B+16+=+4%2A%28x%2B5%29
x%2B8%2Asqrt%28x%29%2B+16+=+4x%2B20
-3x%2B8%2Asqrt%28x%29-4=0
3x-8%2Asqrt%28x%29%2B4=0
Look similar to a quadratic equation, let's use a substitution.
Let x=u%5E2.
3u%5E2-8u%2B4=0
This quadratic equation can be factored.
%283u-2%29%28u-2%29=0
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First solution
3u-2=0
3u=2
u=2%2F3
highlight%28x=u%5E2=4%2F9%29
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Second solution
u-2=0
u=2
highlight%28x=u%5E2=4%29
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Let's check the answers.
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First solution: x=4/9
sqrt%28x%29%2B+4+=+2%2Asqrt%28x%2B5%29
sqrt%284%2F9%29%2B4=2%2Asqrt%284%2F9%2B5%29
2%2F3%2B4=2%2Asqrt%284%2F9%2B45%2F9%29
2%2F3%2B12%2F3=2%2Asqrt%2849%2F9%29
14%2F3=2%2A7%2F3
14%2F3=14%2F3
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Second solution: x=4
sqrt%28x%29%2B+4+=+2%2Asqrt%28x%2B5%29
sqrt%284%29%2B+4+=+2%2Asqrt%284%2B5%29
2%2B4=2%2Asqrt%289%29
6=2%2A3
6=6
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Both answers have been checked.