Complete the square in order to solve the following quadratic equation:

x^2 + 6x = −2

To complete square one is basically doing
a
2
+
2
a
b
+
b
2
=
(
a
+
b
)
2

or
a
2
−
2
a
b
+
b
2
=
(
a
−
b
)
2
We can see that
x
2
=
a
2
and
2
a
b
=
6
x
So all we need to condense this into
(
a
+
b
)
2
is a
b
2
term
We know that
2
b
=
6
as
x
=
a

so
b
=
3

and
b
2
=
9
So if we put the
b
2
term in we get
x
2
+
6
x
+
9
−
9
=
(
x
+
3
)
2
−
9
We include the
±
9
because we have to net add nothing to the equation so
9
−
9
=
0
so we really haven't added anything