First move the constant to the other side of the equation by adding 3 to both sides...
x^2+4x=3
Now halve the linear coefficient, 4/2=2, square it, 2^2=4, and add that value to both sides...
x^2+4x+4=7, now the left side is a perfect square of the form...
(x+2)^2=7, now take the square root of both sides...
x+2=±√7, subtract 2 from both sides...
x=-2±√7
So x=-2-√7 and -2+√7
