Question 313511
I assume you mean, "solve the following by completing the square:"
3x^2 - 2x + 1 = 5
:
3x^2 - 2x + ___ = 5 - 1
:
3x^2 - 2x + ___ = 4
Coefficient of x^2 has to be 1, divide by 3:
x^2 - {{{2/3}}}x + ___ = {{{4/3}}}
Find the third term to complete the square
x^2 - {{{2/3}}}x + {{{1/9}}} = {{{4/3}}} + {{{1/9}}}
:
x^2 - {{{2/3}}}x + {{{1/9}}} = {{{12/9}}} + {{{1/9}}}
:
x^2 - {{{2/3}}}x + {{{1/9}}} = {{{13/9}}}
:
(x - {{{1/3}}})^2 = {{{13/9}}} 
:
x - {{{1/3}}} = +/-{{{sqrt(13/9)}}}
Two solutions
x = {{{1/3}}} + {{{sqrt(13/9)}}} 
x = {{{1/3}}} + {{{(1/3)sqrt(13)}}} 
x = {{{(1 + sqrt(13))/3}}} 
and
x = {{{1/3}}} - {{{sqrt(13/9)}}} 
x = {{{1/3}}} - {{{(1/3)sqrt(13)}}} 
x = {{{(1 - sqrt(13))/3}}}