SOLUTION: Solve by completing the square x^2+4x-3=0

Solve by completing the square 
x² + 4x - 3 = 0

1.  Get into the form 

(variable)² + (coefficient)(variable) =  (a number)

To get 

     x² + 4x - 3 = 0

into that form all we need do is add +3 to both
sides, giving

         x² + 4x = 3

Now we skip a space after the left and right sides
because we are going to be adding something to both
sides and need blanks on both sides to write it in.

   x² + 4x + ___ = 3 + ___

Now we have to stop and figure out what number we must
put in the blanks.  To find out, out to the side or on
scratch paper, follow these instructions:

I. Multiply the coefficient of x by one half, which in 
this case is multiplying 4 by one-half, which gives 
4*(1/2) or 2.    

II. Square that number which means to multiply it by 
itself. 

In this case we square 2 by multiplying it by 
itself and getting 2×2 or 4.  

III. Write that number in both blanks.     

In this case that number is 4, the number which goes 
in both blanks of:

   x² + 4x + ___ = 3 + ___

So this now becomes

   x² + 4x +  4  = 3 +  4 .

Or, upon erasing the blanks which are now filled,
we have:

     x² + 4x + 4 = 3 + 4
  
2. The left side will factor as the product of a 
binomial times itself.

In our case, the left side factors as (x + 2)(x + 2), 
which is the product of a binomial by itself, and 
the right side is just 7, we now have

  (x + 2)(x + 2) = 7

We can write that left side as the square of (x + 2)
or (x + 2)², so now we have:

        (x + 2)² = 7

3. Use the principle of square roots to break that into the
   disjunction of two equations:

By the principle of square roots, an equation of the form 
A² = B is equivalent to the disjunction of two equations,
     _          _
A = ÖB OR A = -ÖB 

So using that principle of taking square roots of both 
sides:
                   
        (x + 2)² = 7

is now equivalent to this disjunction:
           _                _
  x + 2 = Ö7  OR  x + 2 = -Ö7

Solving them we have
               _              _ 
     x = -2 + Ö7 OR x = -2 - Ö7

Oftentimes, to save writing people just write
               _
     x = -2 ± Ö7

Edwin