Answer:
Step-by-step explanation:
Use the quadratic formula to find the solutions.
−
b
±
√
b
2
−
4
(
a
c
)
2
a
-
b
±
b
2
-
4
(
a
c
)
2
a
Substitute the values
a
=
2
a
=
2
,
b
=
−
6
b
=
-
6
, and
c
=
5
c
=
5
into the quadratic formula and solve for
x
x
.
6
±
√
(
−
6
)
2
−
4
⋅
(
2
⋅
5
)
2
⋅
2
6
±
(
-
6
)
2
-
4
⋅
(
2
⋅
5
)
2
⋅
2
Simplify.
Tap for fewer steps...
Simplify the numerator.
Tap for fewer steps...
Raise
−
6
-
6
to the power of
2
2
.
x
=
6
±
√
36
−
4
⋅
2
⋅
5
2
⋅
2
x
=
6
±
36
-
4
⋅
2
⋅
5
2
⋅
2
Multiply
−
4
-
4
by
2
2
.
x
=
6
±
√
36
−
8
⋅
5
2
⋅
2
x
=
6
±
36
-
8
⋅
5
2
⋅
2
Multiply
−
8
-
8
by
5
5
.
x
=
6
±
√
36
−
40
2
⋅
2
x
=
6
±
36
-
40
2
⋅
2
Subtract
40
40
from
36
36
.
x
=
6
±
√
−
4
2
⋅
2
x
=
6
±
-
4
2
⋅
2
Rewrite
−
4
-
4
as
−
1
(
4
)
-
1
(
4
)
.
x
=
6
±
√
−
1
⋅
4
2
⋅
2
x
=
6
±
-
1
⋅
4
2
⋅
2
Rewrite
√
−
1
(
4
)
-
1
(
4
)
as
√
−
1
⋅
√
4
-
1
⋅
4
.
x
=
6
±
√
−
1
⋅
√
4
2
⋅
2
x
=
6
±
-
1
⋅
4
2
⋅
2
Rewrite
√
−
1
-
1
as
i
i
.
x
=
6
±
i
⋅
√
4
2
⋅
2
x
=
6
±
i
⋅
4
2
⋅
2
Rewrite
4
4
as
2
2
2
2
.
x
=
6
±
i
⋅
√
2
2
2
⋅
2
x
=
6
±
i
⋅
2
2
2
⋅
2
Pull terms out from under the radical, assuming positive real numbers.
x
=
6
±
i
⋅
2
2
⋅
2
x
=
6
±
i
⋅
2
2
⋅
2
Move
2
2
to the left of
i
i
.
x
=
6
±
2
i
2
⋅
2
x
=
6
±
2
i
2
⋅
2
Multiply
2
2
by
2
2
.
x
=
6
±
2
i
4
x
=
6
±
2
i
4
Simplify
6
±
2
i
4
6
±
2
i
4
.
x
=
3
±
i
2
x
=
3
±
i
2
The final answer is the combination of both solutions.
x
=
3
2
+
i
2
,
3
2
−
i
2
x
=
3
2
+
i
2
,
3
2
-
i
2
