Question 432931
I need help completing the square of a quadratic equation. ]
3x^2 + x - {{{1/2}}} = 0 
We need the coefficient of x^2 to be 1, divide equation by 3, then we have
x^2 + {{{1/3}}}x - {{{1/6}}} = 0
:
x^2 + {{{1/3}}}x + ____ =  {{{1/6}}}
Find the value to complete the square; {{{(1/2*1/3)^2}}} = {{{1/36}}}
x^2 + {{{1/3}}}x + {{{1/36}}} =  {{{1/6}}} + {{{1/36}}}
x^2 + {{{1/3}}}x + {{{1/36}}} =  {{{6/36}}} + {{{1/36}}}
x^2 + {{{1/3}}}x + {{{1/36}}} =  {{{7/36}}}
Which is
{{{(x + 1/6)^2}}} = {{{7/36}}}
Find the square root of both sides
x + {{{1/6}}} = +/-{{{sqrt(7/36)}}}
extract the perfect square
x + {{{1/6}}} = +/-{{{(1/6)sqrt(7)}}}
Two solutions
x = {{{-1/6}}} + {{{(1/6)sqrt(7)}}}
and
x = {{{-1/6}}} - {{{(1/6)sqrt(7)}}}
we can write it
x = {{{(-1+sqrt(7))/6}}}
and
x = {{{(-1-sqrt(7))/6}}}