Question 1449
2x^2 + 5x +3 = 0
divide everything by 2 to isolate the x^2.  
{{{x^2+5/2x+3/2=0}}}
then use the additive inverse to subtract 3/2. resulting in ...
{{{x^2+5/2x=-3/2}}}
then take half of the X coeffecient (not the x squared)
{{{5/2}}} >>>>> {{{5/2}}}/2 >>> {{{5/4}}}.  <<< square this value.  {{{25/26}}}
then add this value ({{{25/16}}}) to both sides
{{{x^2+5/2x+25/16=-3/2+25/16}}} >> {{{x^2+5/2x+25/16=1/16}}} 
the factor out the first part of the equation before the equal sign.  
{{{(x+5/4)(x+5/4)=1/16}}}
now take the square root of both sides.  
{{{sqrt((x+5/4)(x+5/4))=sqrt(1/16)}}} equals
x+5/4 = +- squareroot of 1 over 4 (i`m sorry for not putting it in a formula, but it wouldn't let me)
then to isolate x, you subtract 5/4 from both sides. resulting in
{{{x=-5/4+-sqrt(1)/4}}}