Question 1086727
<pre>
{{{sqrt(2x+3i)+x=2}}}
Isolate the square root by subtracting x fom both sides:

{{{sqrt(2x+3i)=2-x}}}

Square both sides:

{{{2x+3i=4-4x+x^2}}}

Get 0 on one side:

{{{-x^2+6x-4+3i=0}}}

Multiply through by -1 to get the x<sup>2</sup> term positive:

{{{x^2-6x+4-3i=0}}}

Use the quadratic formula with
a=1, b=-6 and c=4-3i

 {{{x = (-(-6) +- sqrt((-6)^2-4(1)(4-3i)))/(2(1)) }}} 

 {{{x = (6 +- sqrt(36-4(4-3i)))/2 }}}

 {{{x = (6 +- sqrt(36-16+12i))/2 }}}

 {{{x = (6 +- sqrt(20+12i))/2 }}}

 {{{x = (6 +- sqrt(4(5+3i)))/2 }}}

 {{{x = (6 +- 2sqrt(5+3i))/2 }}}

 {{{x = (2(3 +- sqrt(5+3i)))/2 }}}

 {{{x = (cross(2)(3 +- sqrt(5+3i)))/cross(2) }}}

 {{{x = 3 +- sqrt(5+3i) }}}

Checking with a TI-84 calculator in a+bi MODE,

Only  {{{x = 3 - sqrt(5+3i) }}} checks

Edwin</pre>