Answer:3,1
Step-by-step explanation:Subtract
3
3
from both sides of the equation.
x
2
−
4
x
=
−
3
x
2
-
4
x
=
-
3
To create a trinomial square on the left side of the equation, find a value that is equal to the square of half of
b
b
.
(
b
2
)
2
=
(
−
2
)
2
(
b
2
)
2
=
(
-
2
)
2
Add the term to each side of the equation.
x
2
−
4
x
+
(
−
2
)
2
=
−
3
+
(
−
2
)
2
x
2
-
4
x
+
(
-
2
)
2
=
-
3
+
(
-
2
)
2
Simplify the equation.
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Raise
−
2
-
2
to the power of
2
2
.
x
2
−
4
x
+
4
=
−
3
+
(
−
2
)
2
x
2
-
4
x
+
4
=
-
3
+
(
-
2
)
2
Simplify
−
3
+
(
−
2
)
2
-
3
+
(
-
2
)
2
.
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Raise
−
2
-
2
to the power of
2
2
.
x
2
−
4
x
+
4
=
−
3
+
4
x
2
-
4
x
+
4
=
-
3
+
4
Add
−
3
-
3
and
4
4
.
x
2
−
4
x
+
4
=
1
x
2
-
4
x
+
4
=
1
Factor the perfect trinomial square into
(
x
−
2
)
2
(
x
-
2
)
2
.
(
x
−
2
)
2
=
1
(
x
-
2
)
2
=
1
Solve the equation for
x
x
.
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Take the
square
square
root of each side of the
equation
equation
to set up the solution for
x
x
(
x
−
2
)
2
⋅
1
2
=
±
√
1
(
x
-
2
)
2
⋅
1
2
=
±
1
Remove the perfect root factor
x
−
2
x
-
2
under the radical to solve for
x
x
.
x
−
2
=
±
√
1
x
-
2
=
±
1
Any root of
1
1
is
1
1
.
x
−
2
=
±
1
x
-
2
=
±
1
The complete solution is the result of both the positive and negative portions of the solution.
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First, use the positive value of the
±
±
to find the first solution.
x
−
2
=
1
x
-
2
=
1
Move all terms not containing
x
x
to the right side of the equation.
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Add
2
2
to both sides of the equation.
x
=
1
+
2
x
=
1
+
2
Add
1
1
and
2
2
.
x
=
3
x
=
3
Next, use the negative value of the
±
±
to find the second solution.
x
−
2
=
−
1
x
-
2
=
-
1
Move all terms not containing
x
x
to the right side of the equation.
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Add
2
2
to both sides of the equation.
x
=
−
1
+
2
x
=
-
1
+
2
Add
−
1
-
1
and
2
2
.
x
=
1
x
=
1
The complete solution is the result of both the positive and negative portions of the solution.
x
=
3
,
1
x
=
3
,
1
