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\[0={x}^{2}-4x-8\]
+
−
.
ln
>
<
×
÷
/
log
≥
≤
(
)
log
x
=
%
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0=x^2-4x-8
0=x^2-4x-8
0={x}^{2}-4x-8
1
Switch sides.
x
2
−
4
x
−
8
=
0
{x}^{2}-4x-8=0
x
2
−
4
x
−
8
=
0
2
Use the Quadratic Formula.
1
In general, given
a
x
2
+
b
x
+
c
=
0
a{x}^{2}+bx+c=0
a
x
2
+
b
x
+
c
=
0
, there exists two solutions where:
x
=
−
b
+
b
2
−
4
a
c
2
a
,
−
b
−
b
2
−
4
a
c
2
a
x=\frac{-b+\sqrt{{b}^{2}-4ac}}{2a},\frac{-b-\sqrt{{b}^{2}-4ac}}{2a}
x
=
2
a
−
b
+
b
2
−
4
a
c
,
2
a
−
b
−
b
2
−
4
a
c
2
In this case,
a
=
1
a=1
a
=
1
,
b
=
−
4
b=-4
b
=
−
4
and
c
=
−
8
c=-8
c
=
−
8
.
x
=
4
+
(
−
4
)
2
−
4
×
−
8
2
,
4
−
(
−
4
)
2
−
4
×
−
8
2
{x}^{}=\frac{4+\sqrt{{(-4)}^{2}-4\times -8}}{2},\frac{4-\sqrt{{(-4)}^{2}-4\times -8}}{2}
x
=
2
4
+
(
−
4
)
2
−
4
×
−
8
,
2
4
−
(
−
4
)
2
−
4
×
−
8
3
Simplify.
x
=
4
+
4
3
2
,
4
−
4
3
2
x=\frac{4+4\sqrt{3}}{2},\frac{4-4\sqrt{3}}{2}
x
=
2
4
+
4
3
,
2
4
−
4
3
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x
=
4
+
4
3
2
,
4
−
4
3
2
x=\frac{4+4\sqrt{3}}{2},\frac{4-4\sqrt{3}}{2}
x
=
2
4
+
4
3
,
2
4
−
4
3
3
Simplify solutions.
x
=
2
(
1
+
3
)
,
2
(
1
−
3
)
x=2(1+\sqrt{3}),2(1-\sqrt{3})
x
=
2
(
1
+
3
)
,
2
(
1
−
3
)
Done
Decimal Form: 5.464102, -1.464102
x=2*(1+sqrt(3)),2*(1-sqrt(3))
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