SOLUTION: Find the real and complex solution of the equation{{{x^2-8=0}}}

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Question 73561: Find the real and complex solution of the equationx%5E2-8=0
Found 2 solutions by bucky, johnpickett:
Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2+-+8+=+0
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For this problem the easiest way to do it is to add 8 to both sides. Then the problem becomes
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x%5E2+=+8
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Then just take the square root of both sides and you get
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x+=+sqrt%288%29 and x+=+-sqrt%288%29
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The square root of 8 can be simplified by factoring it into sqrt%284%2A2%29 which can then
be written as sqrt%284%29%2Asqrt%282%29. Since sqrt%284%29=+2+ you can substitute 2 for sqrt%284%29
to get that sqrt%288%29+=+2%2Asqrt%282%29
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So the answer simplifies to:
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x+=+2%2Asqrt%282%29 and x+=+-2%2Asqrt%282%29
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There are no complex factors involved here.
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The only thing you have to be careful with in solving this problem is to recognize
that the value for x has to be either plus or minus because if you square them both the
plus and minus values will return a positive value. Squaring:
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2%2Asqrt%282%29 and -2%2Asqrt%282%29
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will both compute to be +8. Therefore either of these will satisfy the equation.
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Hope this helps you with this problem.

Answer by johnpickett(2) About Me  (Show Source):