Solve for x the equation square root(x^2+x+1)=3-x

We notice that we don't have to determine the values of x
for the square root to exist, because the expression x^2+x+1 is positive for any value
of x.

We'll raise to square both
sides:

x^2 + x + 1 =
(3-x)^2

We'll expand the
square:

x^2 + x + 1 = 9 - 6x +
x^2

We'll shift all terms to one
side:

x^2 + x + 1 - 9 + 6x - x^2 =
0

We'll eliminate like
terms:

7x - 8 = 0

We'll
isoalte 7x to the left:

7x =
8

x = 8/7

The
solution of the equation is x = 8/7.