x² + x = 3

Multiply the coefficient of x, which is  by , getting .
Now square , getting  = 

Add + to both sides of the equation:

x² + x +  = 3 + 

The left side will now factor as (x + )(x + ) or (x + )².  So we have:

(x + )² = 3 + 

We will combine the terms on the right by getting the LCD of 16.
Then 3 +  becomes  +  or .
So we now have:

(x + )² = 

Next we use the principle of square roots:

x +  = ±

x +  = ±

Solve for x by adding  to both sides:

      x =  ± 

or you can write it:

      x = 

Edwin