x2-15x+56=0 answer please
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Answer:
How do you solve
x
2
+
15
x
+
56
=
0
?
AlgebraComparing Methods for Solving Quadratics
x
=
−
7
or
x
=
−
8
Explanation:
Find a pair of factors of
56
with sum
15
.
The pair
7
,
8
works in that
7
⋅
8
=
56
and
7
+
8
=
15
Hence:
0
=
x
2
+
15
x
+
56
=
(
x
+
7
)
(
x
+
8
)
So:
x
=
−
7
or
x
=
−
8
Alternative method
I will use the difference of squares identity:
a
2
−
b
2
=
(
a
−
b
)
(
a
+
b
)
with
a
=
(
2
x
+
15
)
and
b
=
1
as follows:
First multiply the whole equation by
4
(to cut down on the use of fractions) to get:
0
=
4
x
2
+
60
x
+
224
=
(
2
x
+
15
)
2
−
225
+
224
=
(
2
x
+
15
)
2
−
1
2
=
(
(
2
x
+
15
)
−
1
)
(
(
2
x
+
15
)
+
1
)
=
(
2
x
+
14
)
(
2
x
+
16
)
=
(
2
(
x
+
7
)
)
(
2
(
x
+
8
)
)
=
4
(
x
+
7
)
(
x
+
8
)
Hence
x
=
−
7
or
x
=
−
8
Step-by-step explanation:
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