Question 193762
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So far, so good.  Now take the square root of both sides, remembering to consider both the positive and negative roots:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \sqrt{(a+7)^2}=\pm\sqrt{17}]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ a + 7 = \pm\sqrt{17}]


Now add -7 to both sides:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ a = -7 \pm\sqrt{17}]


In other words:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ a = -7 + \sqrt{17}]


or


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ a = -7 - \sqrt{17}]


Done.  Unless you are required to provide a numerical approximation.  In that case, get out your calculator.


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