When solving for x by completing the square as in the equation 3(x-1)^2-1=0 should I add one to both sides then divide by three or add one to both sides then square root both sides? It makes sense to me to first divide by three, but if I do this, I'm not getting the correct answer; the correct answer is supposed to be (3+sqrt3)/3 and (3-sqrt3)/3.

Question

I really don't understand how to get this answer or if I'm performing the needed steps in the correct order, please help me understand this.

Answer 1

add one to each side, then divide by three. then take the square root of either side.

methodabove:
x-1=sqrt1/3
x= 1+sqrt 1/3 or 1-sqrt1/3
Note: this is exactly 3/3 +- sqrt 1/3 which is the answer above.

Now, you will find the same if you divide by three first.

(x-1)^2-1/3=0 then add 1/3 to each side.

Answer 2

oh okay, yeah, that's the answer I got, but I'm just still really confused as to how they even got sqrt3. Thank you, though.

Answer 3

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Answer 4

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