slove for x : x2 +3x +9=0
Answers
Not that standard form is
y
=
a
x
2
+
b
x
+
c
and that vertex form is
y
=
a
(
x
+
b
2
a
)
2
+
c
+
k
where
k
is a correction constant in your case
a
=
1
'~~~~~~~~~~~~~~~~~~~~~~~~~~~
Given:
y
=
x
2
+
3
x
−
9
=
0
write as:
0
=
(
x
2
+
3
x
)
−
9
Add the correction constant
k
0
=
(
x
2
+
3
x
)
−
9
+
k
Remove the
x
from
3
x
0
=
(
x
2
+
3
)
−
9
+
k
Halve the 3
0
=
(
x
2
+
3
2
)
−
9
+
k
Move the power from
x
2
to outside the bracket
0
=
(
x
+
3
2
)
2
−
9
+
k
←
the error comes from
a
(
3
2
a
)
2
but
k
+
(
3
2
)
2
=
0
⇒
k
=
−
9
4
giving
Vertex form
→
0
=
(
x
+
3
2
)
2
−
45
4
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Take the
−
45
4
to the other side of the equals and change its sign.
(
x
+
3
2
)
2
=
+
45
4
Square root both sides
x
+
3
2
=
√
45
4
Move the
3
2
to the other side of =
x
=
−
3
2
±
√
5
×
9
√
4
x
=
−
3
2
±
3
√
5
2
x
≈
1.854
and
−
4.854
Hey !!
Here's your answer !!
2x+3x+9=0
5x+9=0
5x=-9
x=-9/5
Hope it helps !!
Thank you:)