Question 949547
{{{6x^2-2x+9}}} this is the quadratic expression 
 
and the quadratic equation in the standard form is 


 {{{f(x)=6x^2 -2x + 9}}}

 {{{f(x)=(6x^2 -2x+_)-_ + 9 }}}

{{{ f(x)=6(x^2 -(1/3)x+_)-_ + 9}}} ...we need to complete the square-recall {{{(a+b)^2=a^2+2ab+b^2}}}

so, use {{{2ab}}} to find {{{b}}}- > 
{{{a=1}}} ->{{{2*1*b=1/3}}}
=>{{{2b=1/3}}}=
>{{{b=(1/3)/2}}}
=>{{{b=1/6}}}
add b and subtract b like this

 {{{f(x)=6(x^2 -2x+(1/6)^2)-6(1/6)^2+ 9}}}

 {{{f(x)=6(x -1/6)^2-6*(1/36)+9}}}

{{{f(x)=6(x -1/6)^2-1/6+(9*6)/6}}}

{{{f(x)=6(x -1/6)^2-1/6+54/6}}}

{{{f(x)=6(x-1/6)^2+53/6}}}