Problema Solution

If 6 times a number is decreased by 2, the principle square root of this difference is 3 less than the number. Find the number(s).

I was taking a test and got it wrong the answer is 11 and I don't understand how they got the answer, this is for an online class..

Please help

Answer provided by our tutors

let x = the number


6x - 2 = (x - 3)^2


and x - 3 > 0 since it is the principle square root


by solving we find


x = 11


x = 1 is not the answer because x - 3 = 1 - 3 = -2 < 0 and we need x - 3 >0


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indeed


6*11 - 2 = 64 = 8^2 = (11 - 3)^2


the number is 11.