Question

y^2-18y-64=0 solve it for y

Answer 1

Explanation:
x
2
+
y
2
−
18
x
−
18
y
+
53
=
0
Use a method called "Completing the Square".
1) Group the x terms and y terms. Move the constant term to the right side of the equation by subtracting 53 from both sides.
(
x
2
−
18
x
a
a
a
)
+
(
y
2
−
18
y
a
a
a
)
=
−
53
2) Divide the coefficient of the x term by 2 and then square it.
−
18
2
=
−
9
a
a
a
(
−
9
)
2
=
81
3) Add the result to both sides.
(
x
2
−
18
x
+
81
)
+
(
y
2
−
18
y
a
a
a
)
=
−
53
+
81
4) Divide the coefficient of the y term by 2 and then square it.
−
18
2
=
−
9
a
a
a
(
−
9
)
2
=
81
5) Add the result to both sides.
(
x
2
−
18
x
+
81
)
+
(
y
2
−
18
y
+
81
)
=
−
53
+
81
+
81
Factor each set of parentheses. Note that the
−
9
in factored form is the same number you got when dividing the coefficient of the middle term.
(
x
−
9
)
(
x
−
9
)
+
(
y
−
9
)
(
y
−
9
)
=
109
Rewrite as the square of a binomial.
(
x
−
9
)
2
+
(
y
−
9
)
2
=
109
Compare this equation to the equation of a circle
(
x
−
h
)
2
+
(
y
−
k
)
2
=
r
2

where
(
h
,
k
)
is the center and
r
is the radius.
In this example, the center
(
h
,
k
)
=
(
9
,
9
)
and the radius
r
=
√
109