Answer for
14
=
2
x
^2
+
x
Step-by-step explanation:
Rewrite the equation as 2
x^
2
+
x=
14
.
2
x
^2
+
x
=
14
Move 14 to the left side of the equation by subtracting it from both sides.
2
x
^2
+
x
−
14
=
0
Use the quadratic formula to find the solutions.
−
b
±
√
b
^2
−
4
(
a
c
)
2
a
Substitute the values a
=
2
, b
=
1
, and c
=
−
14 into the quadratic formula and solve for x
.
−
1
±
√
1
2
−
4
⋅
(
2
⋅
−
14
)
2
⋅
2
Simplify the numerator.
x
=
−
1
±
√
113
2
⋅
2
Multiply 2 by 2
.
x
=
−
1
±
√
113
4
The final answer is the combination of both solutions.
x
=
−
1
−
√
113
- 1
+
√
113
4 4
The result can be shown in multiple forms.
Exact Form:
x
=
−
1
−
√
113
, −
1
+
√
113
4
4 4
Decimal Form:
x
=
2.40753645
… , −
2.90753645
…
