Question 221970
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You did the completion of the square correctly.  The only problem you have is in the simplification of your answer.


You have:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ -2\ \pm\ \sqrt{\frac{7}{2}}]


Which IS a correct answer, it just isn't in simplest form.  The problem is that the denominator of the fraction in the irrational part of the answer is irrational.  You need to rationalize the denominator, thus:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ -2\ \pm\ \sqrt{\frac{7}{2}}\ =\ -2\ \pm\ \left(\frac{\sqrt{7}}{sqrt{2}}\right)\left(\frac{\sqrt{2}}{\sqrt{2}}\right)\ = -2\ \pm\ \frac{\sqrt{14}}{2}]


Which I suspect matches your book's answer.


For more on this subject, see my lesson on rationalizing denominators:


http://www.algebra.com/algebra/homework/Radicals/rationalizingdenominators1.lesson


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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