.What is the value of a ? You should then multiply ( − 8 x − 3 ) and ( a x − 2 ) using FOIL. Since the coefficients of the x 2 -term have to be equal on both sides of the equation, − 8 a = 24 , or a = − 3 .
Answers
Explanation:
:
First, transpose 6 to the other side so the equation would end up in standard form (
a
x
2
+
b
x
+
c
).
4
x
2
+
5
x
−
6
Here, we can use the quadratic formula which is
−
b
±
√
b
2
−
4
a
c
2a
.
We have to find out the variables
a
,
b
, and
c
.
a
=
4
b
=
5
c
=
−
6
We substitute them to the formula and then do the math.
Solve until you stop here with this answer:
−
5
±
√
121
8
.
The square root of 121 is 11, so we end up with:
−
5
±
11
8
.
We then do the arithmetic,
−
5
+
11
and
−
5
−
11
.
The answers are
6
and
−
16
respectively.
Here we end up with
6
8
and
−
16
8
. We then reduce them to simplest form.
x
=
3
4
,
−
2
.
If you want to check, substitute your solutions (the answers) to your formula:
Substituting
x
=
−
2
,
4
(
−
2
)
2
+
5
(
−
2
)
=
6
16
−
10
=
6
6
=
6
Substituting
x
=
3
4
,
4
(
3
4
)
2
+
5
(
3
4
)
=
6
4
(
9
16
)
+
(
15
4
)
=
6
9
4
+
15
4
=
6
24
4
=
6
6
=
6
The both solutions work because the equation is true (
6
=
6
).
Take note that all solutions might not work because they might end up undefined. If all solutions do not work, then there is no solution.
There you go! Hope this helps!
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