How do you solve by completing the square: #x^2+6x+4=0#?

1 Answer
Apr 3, 2015

Solving a quadratic expression by completing the square means to manipulate the expression in order to write it in the form
#(x+a)^2=b#
So, if #b\ge 0#, you can take the square root at both sides to get
#x+a=\pm\sqrt{b}#
and conclude #x=\pm\sqrt{b}-a#.

Now, we have #(x+a)^2=x^2+2ax+a^2#. Since you equation starts with #x^2+6x#, this means that #2ax=6x#, and so #a=3#.
Adding #5# at both sides, we have
#x^2+6x+9=5#
Which is the form we wanted, because now we have
#(x+3)^2=5#
Which leads us to
#x+3=\pm\sqrt{5}# and finally #x=\pm\sqrt{5}-3#