Question 51340
2x^2+6x-2=0
first eliminate (x^2)'s coefficient by dividing both sides with 2
x^2+3x-1=0


then take x's coefficient (3) divide it with 2 now you have one and a half {{{3/2}}}. and take {{{3/2}}}'s square we have {{{9/4}}}. so in order to have a perfect square we need to convert (-1) to {{{9/4}}}. we will do it by adding 1 + {{{9/4}}} to each side which is equal to {{{13/4}}}


{{{x^2+3x+(9/4)=13/4}}}
(x+(3/2))^2=13/4
{{{x+(3/2)= +- sqrt (13/4)}}}
{{{x=( +- sqrt(13) /2)-(3/2)}}}
{{{x=( +- sqrt(13) -3)/2}}}

now we will find two possible answers;


{{{x=(+sqrt(13)-3)/2}}}

and

{{{x=(-sqrt(13)-3)/2}}}