SOLUTION: Find the solution set {{{(3x-1)^2=12}}}

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Question 140623: Find the solution set %283x-1%29%5E2=12
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%283x-1%29%5E2=12 Start with the given equation


3x-1=0%2B-sqrt%2812%29 Take the square root of both sides


Break up the expression and simplify

3x-1=2%2Asqrt%283%29 or 3x-1=-2%2Asqrt%283%29


Add 1 to both sides in each case

3x=2%2Asqrt%283%29%2B1 or 3x=-2%2Asqrt%283%29%2B1


Divide both sides by 3 to isolate x in each case

x=%282%2Asqrt%283%29%2B1%29%2F3 or x=%28-2%2Asqrt%283%29%2B1%29%2F3


Rearrange the terms (this step is not necessary, but you're most likely to see the answer in this format)


x=%281%2B2%2Asqrt%283%29%29%2F3 or x=%281-2%2Asqrt%283%29%29%2F3



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Answer:

So the solution set is exactly

x=%281%2B2%2Asqrt%283%29%29%2F3 or x=%281-2%2Asqrt%283%29%29%2F3

which is approximately

x=1.48803 or x=-.82137