Question 89134
Given:
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{{{(x-1)^2 = 7}}}
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Take the square root of both sides to get:
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{{{x-1 = +sqrt(7)}}} and {{{x-1 = -sqrt(7)}}}
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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 +- sqrt(7)}}}
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So x equals {{{1+sqrt(7)}}} and {{{1 - sqrt(7)}}}
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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 + sqrt(7)}}} for x and the original problem becomes:
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{{{(1 + sqrt(7) - 1)^2 = 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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{{{(sqrt(7))^2 = 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(7)}}} for x and the original problem becomes:
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{{{(1 - sqrt(7) - 1)^2 = 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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{{{(-sqrt(7))^2 = 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!