9
c
−
4
−
c
2
=
−
7
9
c
-
4
-
c
2
=
-
7
Move
7
7
to the left side of the equation by adding it to both sides.
9
c
−
4
−
c
2
+
7
=
0
9
c
-
4
-
c
2
+
7
=
0
Add
−
4
-
4
and
7
7
.
9
c
−
c
2
+
3
=
0
9
c
-
c
2
+
3
=
0
Factor
−
1
-
1
out of
9
c
−
c
2
+
3
9
c
-
c
2
+
3
.
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−
(
c
2
−
9
c
−
3
)
=
0
-
(
c
2
-
9
c
-
3
)
=
0
Multiply each term in
−
(
c
2
−
9
c
−
3
)
=
0
-
(
c
2
-
9
c
-
3
)
=
0
by
−
1
-
1
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c
2
−
9
c
−
3
=
0
c
2
-
9
c
-
3
=
0
Use the quadratic formula to find the solutions.
−
b
±
√
b
2
−
4
(
a
c
)
2
a
-
b
±
b
2
-
4
(
a
c
)
2
a
Substitute the values
a
=
1
a
=
1
,
b
=
−
9
b
=
-
9
, and
c
=
−
3
c
=
-
3
into the quadratic formula and solve for
c
c
.
9
±
√
(
−
9
)
2
−
4
⋅
(
1
⋅
−
3
)
2
⋅
1
9
±
(
-
9
)
2
-
4
⋅
(
1
⋅
-
3
)
2
⋅
1
Simplify.
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c
=
9
±
√
93
2
c
=
9
±
93
2
The final answer is the combination of both solutions.
c
=
9
+
√
93
2
,
9
−
√
93
2
c
=
9
+
93
2
,
9
-
93
2
The result can be shown in multiple forms.
Exact Form:
c
=
9
+
√
93
2
,
9
−
√
93
2
Answer: a=−3
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
a−2+3=−2
a+−2+3=−2
(a)+(−2+3)=−2(Combine Like Terms)
a+1=−2
a+1=−2
Step 2: Subtract 1 from both sides.
a+1−1=−2−1
a=−3
Answer:
SSS
Step-by-step explanation:
Mike has 78 feet of fencing available for his garden, this is the perimeter (P) of the rectangle:
Perimeter: P=78 feet
The formula of Perimeter is:
P=2(W+L), where W is the width and L is the length, then:
P=78→2(W+L)=78
Dividing both sides of the equation by 2:
2(W+L)/2=78/2
W+L=39
If the shape is of a golden rectangle, we know:
L=1.6W
Replacing this above:
W+1.6W=39
Adding similar terms:
2.6W=39
Solving for W
2.6W/2.6=39/2.6
W=15 feet
L=1.6W=1.6(15)→L=24 feet
Answer: T<span>he dimensions of the garden are: Width=15 feet and Length=24 feet. </span>