Question 801034
complete the square: 
4x^2 - 4x - 9 = 0
we want the coefficient of x^2 to be 1, divide eq by 4
x^2 - x - {{{9/4}}} = 0
x^2 - x + __ = {{{9/4}}} 
to complete the square, take half the coefficient of x, and square it
That's (1/2)^2 = 1/4, add to both sides
x^2 - x + {{{1/4}}} = {{{9/4}}} + {{{1/4}}}
x^2 - x + {{{1/4}}} = {{{10/4}}} 
we can write it
{x - {{{1/2}}})^2 = {{{10/4}}}
Find the square root of both sides
x - {{{1/2}}} = +/-{{{sqrt(10/4)}}}
x = {{{1/2}}} +/-{{{sqrt(10/4)}}}
extract the square root of 1/4
x = {{{1/2}}} +/-{{{(1/2)sqrt(10)}}}
write the two solutions as
x = {{{(1+sqrt(10))/2}}}
and
x = {{{(1-sqrt(10))/2}}}