SOLUTION: (x-1)^2=7

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Question 89134: (x-1)^2=7
Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
Given:
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%28x-1%29%5E2+=+7
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Take the square root of both sides to get:
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x-1+=+%2Bsqrt%287%29 and x-1+=+-sqrt%287%29
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Add 1 to both sides to get rid of the -1 on the left side. By adding 1 to both sides
the equation becomes:
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x+=+1+%2B-+sqrt%287%29
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So x equals 1%2Bsqrt%287%29 and 1+-+sqrt%287%29
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You can check these two answers by substituting them for x in the original problem.
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First substitute 1+%2B+sqrt%287%29 for x and the original problem becomes:
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%281+%2B+sqrt%287%29+-+1%29%5E2+=+7
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Notice that within the parentheses the + 1 and the -1 cancel so the equation reduces to:
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%28sqrt%287%29%29%5E2+=+7
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and when you square the square root of 7, the answer is 7 so the equation becomes:
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7+=+7
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and this checks out. So that answer is correct.
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Next substitute 1+-+sqrt%287%29 for x and the original problem becomes:
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%281+-+sqrt%287%29+-+1%29%5E2+=+7
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Notice that within the parentheses the + 1 and the -1 again cancel so the equation
reduces to:
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%28-sqrt%287%29%29%5E2+=+7
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and when you square the negative square root of 7 by multiplying it by the negative
square root of y, the answer is +7 so the equation becomes:
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7+=+7
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and this answer also checks out.
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Hope this helps you to understand the problem. Cheers!