Question 76281
(x-5)^2 = 6
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You are half right.  
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{{{x = 5 + sqrt(6)}}} is correct, but so also is {{{x = 5 - sqrt(6)}}}
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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 {{{(+sqrt(+6))^2 = +6}}} and {{{(-sqrt(+6))^2 = +6}}} also.
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You can verify that {{{x = 5 - sqrt(6)}}} 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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{{{(5 - sqrt(6) - 5)^2 = 6}}}
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Performing the subtraction in the parentheses results in:
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{{{ (- sqrt(6))^2 = 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.