Factorise x^2+6x+5=0 by completing the square.

When completing the square, we first divide the whole equation by the x^2 component. In this case, the x^2 component is 1 so nothing changes. We now apply the method to convert to square form: we reduce the power of x in x^2 and 6x, and half 6x before putting them in brackets to the power 2, i.e [x^(2-1)+(6/2)x^(1-1)]^2. Remember, x^0=1. This simplifies to (x+3)^2. But, if we were to expand these brackets, we would get x^2+6x+9, which is 4 more than x^2+6x+5, so we take away 4. Therefore, our answer in completed square form is (x+3)^2-4=0.