Question 331600
{{{(x-3/2)^2+7/4=0}}}
Subtract 7/4 from both sides
{{{(x-3/2)^2}}} = {{{-7/4}}}
Find square root of both sides
{{{x-3/2}}} = {{{sqrt(-7/4)}}}
:
{{{x-3/2}}} = +/-{{{(1/2)i*sqrt(7)}}}
:
x = {{{3/2}}} +/- {{{(1/2)i*sqrt(7)}}}
Two solutions
x = {{{((3+sqrt(7)i))/2}}}
and
x = {{{((3-sqrt(7)i))/2}}}
:
:
Check:
x = {{{3/2}}} +/-{{{sqrt(7)/2}}}i
x - {{{3/2}}} = +/-{{{sqrt(7)/2}}}i
Square both sides
{{{(x-3/2)^2}}} = {{{7/4}}}i^2
{{{(x-3/2)^2}}} = {{{7/4}}}(-1)
{{{(x-3/2)^2}}} = {{{-7/4}}}
{{{(x-3/2)^2}}} + {{{7/4}}} = 0