SOLUTION: Solve (x-5)^2 = 6 I just need to verify my answer of {{{5+sqrt(6)}}}. Is this correct? Thanks so much for your help.

Algebra ->  Algebra  -> Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: Solve (x-5)^2 = 6 I just need to verify my answer of {{{5+sqrt(6)}}}. Is this correct? Thanks so much for your help.      Log On

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Question 76281: Solve (x-5)^2 = 6
I just need to verify my answer of 5%2Bsqrt%286%29. Is this correct? Thanks so much for your help.
Answer by bucky(2099) About Me  (Show Source):
You can put this solution on YOUR website!
(x-5)^2 = 6
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You are half right.
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x+=+5+%2B+sqrt%286%29 is correct, but so also is x+=+5+-+sqrt%286%29
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When you take the square root of both sides you need to think in terms of two answers,
one positive and one negative.
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This is because %28%2Bsqrt%28%2B6%29%29%5E2+=+%2B6 and %28-sqrt%28%2B6%29%29%5E2+=+%2B6 also.
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You can verify that x+=+5+-+sqrt%286%29 is a solution also by substituting the right side
into the original problem for x. When you do that you get:
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%285+-+sqrt%286%29+-+5%29%5E2+=+6
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Performing the subtraction in the parentheses results in:
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+%28-+sqrt%286%29%29%5E2+=+6
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and this is the same as was explained above.
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When you square a negative number, the result is positive ... so you end up with a positive
6 on both sides.
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Hope this helps you to see why there were two answers to this problem ... the one you
found and the same answer, but with a minus sign between terms.