Question 1083580
Equations are solved by finding easier equivalent equations.
Equivalent equations are equations that have exactly the same solutions.
The equations listed below are all equivalent.
{{{x^2+x+1=0}}}
{{{x^2+x+1/4+3/4=0}}
{{{(x+1/2)^2+3/4=0}}}
There is no real solution to those equations.
For all real values of x,
{{{(x+1/2)^2>=0}}} and {{{(+1/2)+3/4>=3/4}}} .
If you are looking for complex solutions,
{{{(x+1/2)^2=-3/4}}} ,
{{{x+1/2=" " +- i*sqrt(3)/2}}} , and
{{{x=-1/2 +- i*sqrt(3)/2}}}