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−
x
2
+
6
x
−
8
=
3
x
+
7
-{x}^{2}+6x-8=3x+7
−
x
2
+
6
x
−
8
=
3
x
+
7
+
−
.
ln
>
<
×
÷
/
log
≥
≤
(
)
log
x
=
%
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"(x+1)/2+4=7"
"factor x^2+5x+6"
"integrate cos(x)^3"
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-x^2+6x-8=3x+7
-x^2+6x-8=3x+7
-{x}^{2}+6x-8=3x+7
1
Move all terms to one side.
x
2
−
6
x
+
8
+
3
x
+
7
=
0
{x}^{2}-6x+8+3x+7=0
x
2
−
6
x
+
8
+
3
x
+
7
=
0
2
Simplify
x
2
−
6
x
+
8
+
3
x
+
7
{x}^{2}-6x+8+3x+7
x
2
−
6
x
+
8
+
3
x
+
7
to
x
2
−
3
x
+
15
{x}^{2}-3x+15
x
2
−
3
x
+
1
5
.
x
2
−
3
x
+
15
=
0
{x}^{2}-3x+15=0
x
2
−
3
x
+
1
5
=
0
3
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
=
−
3
b=-3
b
=
−
3
and
c
=
15
c=15
c
=
1
5
.
x
=
3
+
(
−
3
)
2
−
4
×
15
2
,
3
−
(
−
3
)
2
−
4
×
15
2
{x}^{}=\frac{3+\sqrt{{(-3)}^{2}-4\times 15}}{2},\frac{3-\sqrt{{(-3)}^{2}-4\times 15}}{2}
x
=
2
3
+
(
−
3
)
2
−
4
×
1
5
,
2
3
−
(
−
3
)
2
−
4
×
1
5
3
Simplify.
x
=
3
+
51
ı
2
,
3
−
51
ı
2
x=\frac{3+\sqrt{51}\imath }{2},\frac{3-\sqrt{51}\imath }{2}
x
=
2
3
+
5
1
,
2
3
−
5
1
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x
=
3
+
51
ı
2
,
3
−
51
ı
2
x=\frac{3+\sqrt{51}\imath }{2},\frac{3-\sqrt{51}\imath }{2}
x
=
2
3
+
5
1
,
2
3
−
5
1
Done
x=(3+sqrt(51)*IM)/2,(3-sqrt(51)*IM)/2
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