Question 69254
{{{4x^2+2x-3=0}}}Move the -3 to the right side by adding 3 to both sides
{{{4(x^2+(2/4)x)=3}}}Factor out a 4 to get leading coefficient equal to 1
{{{4(x^2+(1/2)*x+__)=3}}}Complete the square by taking half of the x coefficient and squaring it {{{((1/2)*(1/2))^2=1/16}}}
{{{4(x^2+(1/2)*x+1/16)=3+4/16}}}add that value to both sides (remember the 4 was factored out, so the complete value should be 4/16 or 1/4)
{{{4(x^2+(1/2)*x+1/16)=3+1/4}}}The left side of the equation then becomes 4(x+1/4)^2 (because if it's foiled it becomes {{{4(x^2+(1/2)*x+1/16)}}} again).
{{{4(x+1/4)^2=12/4+1/4}}}Simplify right side
{{{4(x+1/4)^2=13/4}}}
{{{4(x+1/4)^2=13/4}}}Subtract 13/4 from both sides

{{{(cross(4)*(x+1/4)^2)/cross(4)=(13/4)/4}}}Now you can solve for x by first dividing each side by 4
{{{sqrt((x+1/4)^2)=sqrt(13/16)}}}Then take the square root of both sides
{{{x+1/4=0+-sqrt(13/16)}}}(ignore the zero before the plus/minus)
{{{x+1/4=0+-sqrt(13/16)}}}finally subtract 1/4 from each side
{{{x=0+-sqrt(13/16)-1/4}}}remember the square root of a number is both positive and negative
{{{x=0+-sqrt(13)/4-1/4}}} Add numerators over common denominator
{{{x=(0+-sqrt(13)-1)/4}}} 
So {{{x=(sqrt(13)-1)/4}}} and {{{x=(-sqrt(13)-1)/4}}}
or in decimal form x=0.6514 and x=-1.1514

Note: the completed square can be verified if you graph both {{{4x^2+2x-3=0}}} and {{{4(x+1/4)^2-13/4=0}}} together. Set them up in y form (ex {{{y=4x^2+2x-3}}}) and they should both be the same graph. Hope this helps.