Answer:
Let's apply the quadratic formula:
⇒
x
=
−
4
±
√
4
2
−
4
(
2
)
(
−
30
)
2
(
2
)
⇒
x
=
−
4
±
√
16
+
240
4
⇒
x
=
−
4
±
√
256
4
⇒
x
=
−
4
±
16
4
⇒
x
=
−
1
±
4
⇒
x
=
−
5
,
3
Therefore, the solutions to the equation are
x
=
−
5
and
x
=
3
.
.
Step-by-step explanation:
Step-by-step explanation:
All the terms in the equation are even, so we can divide by 2 immediately to make the numbers smaller.
2
x
2
+
4
x
−
30
=
0
x
2
+
2
x
−
15
=
0
Try to factor before we use loner methods of the quadratic formula or completing the square.
Find factors of 15 which subtract (because of -15) to give 2.
The signs will be different (because of -15), there must be more positives. (because of +2)
5 and 3 will work!
5
×
3
=
15
and
5
−
3
=
2
(
x
+
5
)
(
x
−
3
)
=
0
Putting each factor equal to 0 gives the solutions:
x
=
−
5
or
x
=
3