Question 528072
solve by completing the square? {{{x^2 + 3/2}}}x = 3
:
{{{x^2 + 3/2}}}x + __ = 3
Find the term that will complete the square. Divide the coefficient of x by 2 and square it, add to both sides
{{{x^2 + 3/2}}}x + {{{9/16}}} = 3 + {{{9/16}}}
{{{x^2 + 3/2}}}x + {{{9/16}}} = {{{48/16}}} + {{{9/16}}}
{{{x^2 + 3/2}}}x + {{{9/16}}} = {{{57/16}}}
which is
{{{(x + 3/4)^2}}} = {{{57/16}}}
find the square root of both sides:
{{{(x + 3/4)}}} = +/-{{{sqrt(57/16)}}}
The positive solution
x = {{{-3/4}}} +  {{{sqrt(57/16)}}}
extract the square root of 1/16
x = {{{-3/4}}} +  {{{(1/4)sqrt(57)}}}
Which is
x = {{{(-3+sqrt(57))/4}}}
and the negative solution
x = {{{(-3-sqrt(57))/4}}}