Solve the quadratic equation by completing the square.

x2 + 4x - 3 = 0

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