Answer:
x
2
+
3
x
−
7
=
0
Add
7
to both sides of the equation.
x
2
+
3
x
=
7
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
2
)
2
=
Add
7
to both sides of the equation.
x
2
+
3
x
=
7(
3
2
)
2
Add the term to each side of the equation.
x
2
+
3
x
+
(
3
2
)
2
=
7
+
(
3
2
)
2
Simplify the equation.
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x
2
+
3
x
+
9
4
=
37
4
Factor the perfect trinomial square into
(
x
+
3
2
)
2
.
(
x
+
3
2
)
2
=
37
4
Solve the equation for
x
.
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x
=
±
√
37
2
−
3
2
The result can be shown in multiple forms.
Exact Form:
x
=
±
√
37
2
−
3
2
Decimal Form:
x
=
1.5413812
,
−
4.54138126
Explanation: