Plz answer the following 5 questions by completing the square click on the attachment below to see the questions. SHOW ALL WORK
Answers
Answer:
1. x^2-8x+5=0
Answer:
Root 1
=
4
+
√
11
Root 2
=
4
−
√
11
Explanation:
Given:
x
2
−
8
x
+
5
=
0
The standard form of a quadratic is
a
x
2
+
b
x
+
c
=
0
So, we have
a
=
1
,
b
=
−
8
and
c
=
5
.
Solutions are given by
−
b
±
√
b
2
−
4
a
c
2
a
⇒
−
(
−
8
)
±
√
(
−
8
)
2
−
4
(
1
)
(
5
)
2
⋅
1
Using scientific calculator, we get,
⇒
8
±
√
44
2
[ Intermediate Result 1 ]
Observe that
√
44
can also be simplified as
√
4
⋅
11
⇒
√
2
2
⋅
11
⇒
√
2
2
⋅
√
11
⇒
2
√
11
Now, we can write [ Intermediate Result 1 ] as
8
±
2
√
11
2
We can rewrite the above as
8
2
±
2
√
11
2
4
⋅
2
2
±
2
√
11
2
4
⋅
2
2
±
2
√
11
2
⇒
4
±
√
11
Hence, we have the following two solutions:
Root 1 =4+sqrt(11)
Root 2 =4-sqrt(11)
Using a scientific calculator, we can simplify the above results.
Root 1
≈
7.31662479
Root 2
≈
0.68337521
Step-by-step explanation: