Subtract
6
6
from both sides of the equation.
x
2
−
7
x
=
−
6
x
2
-
7
x
=
-
6
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
=
(
−
7
2
)
2
(
b
2
)
2
=
(
-
7
2
)
2
Add the term to each side of the equation.
x
2
−
7
x
+
(
−
7
2
)
2
=
−
6
+
(
−
7
2
)
2
x
2
-
7
x
+
(
-
7
2
)
2
=
-
6
+
(
-
7
2
)
2
Simplify the equation.
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x
2
−
7
x
+
49
4
=
25
4
x
2
-
7
x
+
49
4
=
25
4
Factor the perfect trinomial square into
(
x
−
7
2
)
2
(
x
-
7
2
)
2
.
(
x
−
7
2
)
2
=
25
4
(
x
-
7
2
)
2
=
25
4
Solve the equation for
x
x
.
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x
=
6
,
1
