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.

Question 76281: Solve (x-5)^2 = 6
I just need to verify my answer of . Is this correct? Thanks so much for your help.
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
(x-5)^2 = 6
.
You are half right.
.
is correct, but so also is
.
When you take the square root of both sides you need to think in terms of two answers,
one positive and one negative.
.
This is because and also.
.
You can verify that is a solution also by substituting the right side
into the original problem for x. When you do that you get:
.

.
Performing the subtraction in the parentheses results in:
.

.
and this is the same as was explained above.
.
When you square a negative number, the result is positive ... so you end up with a positive
6 on both sides.
.
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.
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