SOLUTION: Solve by completing the square 3x^2 – 8x + 2 = 0

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Question 157136: Solve by completing the square 3x^2 – 8x + 2 = 0
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
Solve by completing the square 3x%5E2+%96+8x+%2B+2+=+0

3x%5E2+%96+8x+%2B+2+=+0
Add -2 to both sides:

3x%5E2+-+8x+=+-2

Divide through by coefficient of x%5E2 which is 3

x%5E2+-+8%2F3x+=+-2%2F3

To the side, multiply the coefficient of x,
which is -8%2F3 by 1%2F2, getting -8%2F3*1%2F2=-4%2F3 

Square -4%2F3.  %28-4%2F3%29%5E2=16%2F9. Add 16%2F9 to both
sides

x%5E2+-+8%2F3x+%2B16%2F9=+-2%2F3%2B16%2F9

Factor the left side. Get LCD=9 on the right:

%28x-4%2F3%29%28x-4%2F3%29=+-6%2F9%2B16%2F9

Write left side as a perfect square:
Conbine fractions on the right:

%28x-4%2F3%29%5E2=+10%2F9

Use the principle of square roots:

sqrt%28%28x-4%2F3%29%5E2%29=±sqrt%2810%2F9%29

x-4%2F3=±sqrt%2810%29%2F3

Add 4%2F3 to both sides:

x=4%2F3%2B-sqrt%2810%29%2F3
 
So the two solutions are

4%2F3%2Bsqrt%2810%29%2F3 and 4%2F3-sqrt%2810%29%2F3

Or if you prefer you can write them over their
common denominator:

%284%2Bsqrt%2810%29%29%2F3 and %284-sqrt%2810%29%29%2F3

Edwin